a detailed descrption of reactingtwophaseeulerfoam

Cite as: Cappelli, D.: A detailed description of reactngTwoPhaseEulerFoam focussing on the links between

mass and heat transfer at the phase interface. In Proceedings of CFD with OpenSource Software, 2018,

Edited by Nilsson. H., http://dx.doi.org/10.17196/OS_CFD#YEAR_2018

CFD with OpenSource software

A course at Chalmers University of TechnologyTaught by Hakan Nilsson

A detailed descrption ofreactingTwoPhaseEulerFoam focussing onthe links between mass and heat transfer

at the interface

Developed for OpenFOAM-v1806

Author:Darren CAPPELLIUniversity College [email protected]

Peer reviewed by:Mohammad H. Arabnejad

Ashkhen Nalbandyan

Licensed under CC-BY-NC-SA, https://creativecommons.org/licenses/

Disclaimer: This is a student project work, done as part of a course where OpenFOAM and someother OpenSource software are introduced to the students. Any reader should be aware that it

might not be free of errors. Still, it might be useful for someone who would like learn some detailssimilar to the ones presented in the report and in the accompanying files. The material has gone

through a review process. The role of the reviewer is to go through the tutorial and make sure thatit works, that it is possible to follow, and to some extent correct the writing. The reviewer has no

responsibility for the contents.

December 19, 2018

Learning outcomes

The main requirements of a tutorial is that it should teach the four points: How to use it, Thetheory of it, How it is implemented, and How to modify it. Therefore the list of learning outcomesis organized with those headers.

The reader will learn:

How to use it:

• How to use the reactingTwoPhaseEulerFoam solver.

• The case example will be a laminar bubble column with air and water from the OpenFOAMtutorials.

The theory of it:

• The theory behind two phase flow will be discussed along with the theory of mass and heattransfer at the interface.

• The equations used by OpenFOAM in this solver will be derived from first principles andanalyzed.

How it is implemented:

• The algorithm used in reactingTwoPhaseEulerFoam will be followed in a logical and coherentmanner.

• The equations in the code will be compared to the equations in the theory.

How to modify it:

• A new case set up using methanol as an alternative to water will be described.

• A new saturation model will be developed and implemented.

1

Prerequisites

The reader is expected to know the following in order to get maximum benefit out of this report:

• It is recommended to have a fundamental understanding of the physics behind mass and heattransfer. Chapters 6 and 14 of Fundamentals of heat and mass transfer , Book by Frank.PIncropera, provide a good description of the topics.

• Dimensional groups like Sherwood number,Reynolds,Number,Prandtl Number, Schmidt Num-ber and Lewis Number

• Run standard document tutorials like damBreak tutorial

• The physics of two-phase flows are described in the thesis of, Rusche, H.: Computational FluidDynamics of Dispersed Two-Phase Flows at High Phase Fractions, 2002.

• The following report describes the MULES and PIMPLE algorithm employed in OpenFOAM,Manni, A.:An Introduction to twoPhaseEulerFoam with addition of a heat exchange model.In proceedings of CFD with OpenSourceSoftware, 2014.

• The following report describes the mass transfer models employed in the reactingEulerFoamsolvers, Phanindra.P.Thummala: Description of reactingTwoPhaseEulerFoam solver with afocus on mass transfer modeling terms. In Proceedings of CFD with OpenSource Software,2016.

• The following report describes how the multi-phase system is set up in multiphaseEulerFoam,Surya Kaundinya,O.: Implementation of cavitation models into the multiphaseEulerFoamsolver. In Proceedings of CFD with OpenSource Software, 2017.

2

Contents

1 Theory 5

2 Tutorial Case 82.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.2 Copy from tutorial directory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.3 Boundary and initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2.3.1 Species fractions within phases . . . . . . . . . . . . . . . . . . . . . . . . . . 102.3.2 Phase fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3.3 Pressure and hydrostatic pressure . . . . . . . . . . . . . . . . . . . . . . . . 132.3.4 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.5 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.4 Definition of phase properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.4.1 Definition of phase system and phase models . . . . . . . . . . . . . . . . . . 172.4.2 Blending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192.4.3 Interface Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4.4 Heat transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.4.5 Mass transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.4.6 Surface tension and aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . . 232.4.7 Drag and virtual mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.5 Definition of thermophysical properties . . . . . . . . . . . . . . . . . . . . . . . . . . 252.5.1 Thermodynamic properties of the phase . . . . . . . . . . . . . . . . . . . . . 252.5.2 Species definition within the phase . . . . . . . . . . . . . . . . . . . . . . . . 26

2.6 System set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.7 Run the case and visualize in Paraview . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Classes 303.1 twoPhaseSystem class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.1.1 twoPhaseSystem.H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.1.2 twoPhaseSystem.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.1.3 twoPhaseSystems.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.1.4 newTwoPhaseSystem.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 phaseModel class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.1 phaseModel.H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.2 phaseModel.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2.3 phaseModels.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2.4 newPhaseModel.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.3 InterfaceCompositionPhaseChangePhaseSystem . . . . . . . . . . . . . . . . . . . . . 453.3.1 InterfaceCompositionPhaseChangePhaseSystem.H . . . . . . . . . . . . . . . 453.3.2 InterfaceCompositionPhaseChangePhaseSystem.C . . . . . . . . . . . . . . . 46

3.4 HeatAndMassTransferPhaseSystem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.4.1 HeatAndMassTransferPhaseSystem.H . . . . . . . . . . . . . . . . . . . . . . 533.4.2 HeatAndMassTransferPhaseSystem.C . . . . . . . . . . . . . . . . . . . . . . 55

3

CONTENTS CONTENTS

3.5 Saturation Model Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.5.1 Arden Buck saturation model . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

4 Algorithm 644.1 createFields.H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.2 createFieldRefs.H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 664.3 reactingTwoPhaseEulerFoam.C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.4 YEqns.H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.4.1 MultiComponentPhaseModel.C . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5 Case Modification 725.1 Antoine Equation Manipulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.2 Copying solver to the user directory . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.3 Creating a new saturation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.4 New Case Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.4.1 constant/thermophysicalProperties.gas . . . . . . . . . . . . . . . . . . . . . . 765.4.2 constant/thermophysicalProperties.liquid . . . . . . . . . . . . . . . . . . . . 775.4.3 constant/phaseProperties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.5 Run new case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4

Chapter 1

Theory

This chapter will explain the theory employed by the reactingTwoPhaseEulerFoam solver. In section2.1 it was explained that the solver uses a two-fluid Eulerian model to describe the system, whereboth phases are treated as inter-penetrating continua, Rushe (2002). Below was taken from Rushe’sthesis.

The mean properties of the flow for each phase, ϕ are described by the averaged conservationequations for mass and momentum,

∂αϕUϕ

∂t+∇ · (αϕUϕUϕ) +∇ · (αϕRϕ

eff) = −αϕ

ρϕ∇p+ αϕg +

Mϕ

ρϕ(1.1)

∂αϕ∂t

+∇ · (Uϕαϕ) = 0 (1.2)

where the subscript ϕ denotes the phase, α is the phase fraction, Uϕ is the velocity of the phase,

Rϕeff

is the combined Reynolds and viscous stress, ρϕ is the density of the phase, p is the systempressure, g is the gravitation constant and Mϕ is the averaged inter-phase momentum transfer term.

The averaged inter-phase momentum transfer term is required to ensure conservation of momen-tum. This is required for multi-phase systems as momentum can transfer between phases. Thisterms main contributions are due to drag, lift and virtual mass. However, in the case of mass trans-fer, an extra term is added. This term takes into account the momentum entering and leaving thephase during mass transfer and is defined by the equation below.

¯MMTϕ = ˙mϕIn¯Uϕ−1 − ˙mϕOutUϕ (1.3)

where the subscripts ϕ−1 denotes the other phase, In denotes into the phase, Out denotes out ofthe phase, m is the mass transfer rate and ¯MMTϕ is the mass transfer component of the momentumtransfer term.

For the two-phase system described in chapter 2, both the gas and liquid phases will have theirown momentum conservation equation (equation 1.1). There will be one value for the inter-phasemomentum transfer for the system, however, the sign of the term will vary depending on the direc-tion of momentum transfer.

Weller re-arranged the phase continuity equation 1.2 so that by solving the equation for one phase,the phase fraction αϕ remains bounded between 0 and 1.

∂αϕ∂t

+∇ · (Uαϕ) +∇ · (Urαϕ(1− αϕ)) = 0 (1.4)

5

CHAPTER 1. THEORY

where U = αϕUϕ + αϕ−1 ¯Uϕ−1 and Ur = Uϕ − ¯Uϕ−1 .

The energy equations for each phase are described below,

∂αϕρϕ(Hϕ + Kϕ)

∂t+∇ · (αϕρϕUϕ(Hϕ + Kϕ))−∇ · (αϕαϕeff∇Hϕ) = (1.5)

αϕ∂p

∂t+ ρϕg ·Uϕ + αϕQR + ˙QKD + ˙QTD

where Hϕ denotes the enthalpy of phase ϕ, Kϕ denotes the kinetic energy of phase ϕ, αϕeff denotes

the effective thermal diffusivity of the phase, QR denotes the rate of heat change due to reaction,˙QKE denotes the rate of heat change due to a difference in kinetic energy and ˙QTD denotes the

rate of heat change due to temperature difference. The rate of heat change due to kinetic energydifference and temperature difference are described by the equations below,

˙QKE = ˙mϕIn(Kϕ−1 −Kϕ) (1.6)

˙QTD = hiϕ(Tf − Tϕ) (1.7)

where hiϕ denotes the heat transfer coefficient of species i in phase ϕ, Tf denotes the interfacetemperature and Tϕ denotes the phase temperature.

The above terms take into account the energy effects that mass transfer will have in the system.Transferring mass will carry its own kinetic and heat energy. Equation 1.6 describes the changein kinetic energy for the phase. The heat energy is imparted to the phase through a temperaturedifference with the interface. The temperature at the interface changes as a result of phase changeand depends on the latent heat of the species changing phase. Equation 1.7 describes the change inheat energy for the phase.

The interface temperature is calculated from the assumption that the rate of heat transfer at theinterface must equal the latent heat,λi consumed at the interface.

hiϕ(Tϕ − Tf ) + hiϕ−1(T−1ϕ − Tf ) = ˙mϕInλi (1.8)

As a result of mass transfer occurring in the system, the species transport equation is required todescribe concentration of a species within a phase,

∂αϕCi∂t

+∇ · (αϕUϕCi)−∇αϕDiϕ∇(Ci) = Ri +dmi

dt(1.9)

where subscript i denotes the species, Ci denotes the concentration of the species in kg/m3, Diϕ

denotes the mass diffusion coefficient of species i in phase ϕ, Ri denotes the rate of change in speciesi due to reaction for the phase and dmi

dt denotes the mass transfer of species i in or out of the phase.

For the two-phase system described in chapter 2, each phase has two components, water and air,therefore, each phase will have two species transport equations. In total there will be four speciestransport equations. It should be noted that the water species transport equation for both phaseswill have one value for the mass transfer term, dmi

dt , however, the sign of the term will vary dependingon the direction of mass transfer.

The current form of the equation is not valid for compressible flow, this is because the speciesconcentration, Ci is dependent on volume which is evident from the units of kg/m3. To overcome

6

CHAPTER 1. THEORY

this, OpenFOAM uses a species concentration, Yi which is dependent on mass and has units ofkg/kg. The two species concentrations are related by the equation below.

Yi =Ciρϕ

(1.10)

The mass diffusion coefficient of the component for the phase, Diϕ, is not computed directly. Itis computed through the dimensionless Schmidt number, Sc. The substitution for Diϕ is outlinedbelow.

Diϕ =µϕ

ρϕSciϕ(1.11)

The new species transport equation is achieved by multiplying equation 1.9 byρϕρϕ

, substituting in

equation 1.11 and converting the species concentration to, Yi, using equation 1.10.

∂αϕρϕYi∂t

+∇ · (αϕρϕUϕYi)−∇αϕµϕSciϕ

∇(Yi) =dmi

dt(1.12)

The rate of mass transfer of a component, dmi

dt is described by the equation below.

dmi

dt= kiϕa(C∗

i − Ci) (1.13)

Where kiϕ denotes the mass transfer coefficient of species i in phase ϕ, a denotes the interfacial areafor mass transfer and C∗

i denotes the saturation concentration of species i at the interface of the twophases.

The above equation undergoes a similar manipulation to equation 1.9 and is multiplied byρϕρϕ

.

The species concentration is then converted to, Yi, using equation 1.10.

dmi

dt= ρϕkiϕa(Y ∗

i − Yi) (1.14)

The saturation concentration C∗i is dependent on the temperature of the system and can be predicted

using saturation models. The saturation model will predict the saturation pressure of a componentat the phase interface, p∗i . This saturation pressure is converted to the saturation concentrationusing the ideal gas equation.

C∗i =

MWi

RTp∗i (1.15)

The OpenFOAM conversion used to convert saturation pressure to saturation concentration is amodification of the above equation. The density of the phase, ρϕ is expressed in terms of the idealgas equation.

ρϕ =MWϕ

RTp (1.16)

Substituting equations 1.15 and 1.16 into equation 1.10 yields the equation OpenFOAM use toconvert saturation pressure,p∗i , to saturation concentration,Y ∗

i .

Y ∗i =

MWi

MWϕ

p∗ip

(1.17)

7

Chapter 2

Tutorial Case

2.1 Introduction

This tutorial describes how to prepare and run a case using the reactingTwoPhaseEulerFoam solver.The method involved in a case set up will be outlined and the case files will be described. The theorybehind this solver and the classes employed in it will then be discussed in detail and compared tothe code. Finally, modifications to the solver will be developed and implemented.

The reactingTwoPhaseEulerFoam solver uses a two-fluid Eulerian model to describe the system.The Eulerian two-phase system involves two inter-penetrating continua where each phase is its owncontinuum and is represented by averaged conservation equations. The solver is capable of handlingmulti-component phases and mass and heat transfer between the two phases.

The tutorial case deals with a laminar bubble column containing air and water. The bubble columngeometry will consist of a vertical block filled with water and the remaining head-space will be filledwith air. Figure 2.1 shows the phase distribution for the case at time zero, where the blue representsliquid and the red represents gas. Gas consisting of pure air will enter at the bottom of the column,sparge through the water, and exit at the top of the column. The outlet gas will consist of air andwater. The gas will enter the column at 350 K and 0.1 m/s. The liquid in the column will also beat 350 K and will have no inflow. The pressure within the column will be 1e5 Pa. Both the liquidand gas in the column are multi-component phases; the components being water and air.

As the simulation progresses, the gas phase will become more saturated with water due to masstransfer as the water changes phase from liquid to gas. This solver contains many phase models todescribe the phases; From a basic pure phase model to a more complicated reacting phase model.The solver also allows the user to choose how the phases interact with one another. This can bedone by choosing the phase system which will be described later in the tutorial.

Figure 2.1: Phase fraction of liquid at time 0

8

2.2. COPY FROM TUTORIAL DIRECTORY CHAPTER 2. TUTORIAL CASE

2.2 Copy from tutorial directory

Copy the bubbleColumnEvaporatingDissolving tutorial to the run directory.

1 cp −r $FOAM TUTORIALS/multiphase/reactingTwoPhaseEulerFoam/laminar/bubbleColumnEvaporatingDissolving $FOAM RUN

2 cd $FOAM RUN/bubbleColumnEvaporatingDissolving

The file structure of the bubbleColumnEvaporatingDissolving case is similar to other OpenFOAMtutorials where the case directory has a /0, /constant and /system directory.

2.3 Boundary and initial conditions

The boundary conditions and initial conditions for the case are set in the /0 directory. The variablesare described in Table 2.1.

Variable Notation Variable meaningair.gas Mass fraction of air in the gas phaseair.liquid Mass fraction of air in the liquid phasealpha.gas phase fraction of gasalpha.liquid phase fraction of liquidp Pressurep rgh Pressure without hydrostatic pressureT.gas Temperature of the gas phaseT.liquid Temperature of the liquid phaseU.gas Velocity of gas phaseU.liquid Velocity of liquid phasewater.gas Mass fraction of water in the gas phasewater.liquid Mass fraction of water in the liquid phase

Table 2.1: Boundary condition variables to be set in the /0 directory

9

2.3. BOUNDARY AND INITIAL CONDITIONS CHAPTER 2. TUTORIAL CASE

2.3.1 Species fractions within phases

As described in the introduction this solver supports multi-component phases. In this case only twocomponents/species are present in each phase however, it would be possible to add more species ifrequired. Air and water are said species. The boundary and initial conditions of the species areset in the /0 directory. The files which define these conditions are /0/air.gas, /0/air.liquid,/0/water.gas and /0/water.liquid.

The file /0/air.gas which defines the mass fraction of air in the gas phase is shown below.

1 dimensions [0 0 0 0 0 0 0];23 internalField uniform 1;45 boundaryField6 {7 inlet8 {9 type fixedValue;

10 value $internalField ;11 }12 outlet13 {14 type inletOutlet ;15 phi phi.gas;16 inletValue $internalField ;17 value $internalField ;18 }19 walls20 {21 type zeroGradient;22 }23 }

In the /0/air.gas file, it can be seen that the mass fraction of air in the gas phase is set to 1throughout the internal field of the column. The mass fraction of air in the gas phase is set to 1 atthe inlet boundary condition which means that the inlet gas will be pure air. The outlet boundarycondition is of type inletOutlet which is a generic outflow boundary condition for a specified inletflow. The zero gradient boundary condition is used at the wall. It is evident from line 1 of the abovecode that the air.gas variable is dimensionless.

The files /0/air.liquid, /0/water.gas and /0/water.liquid follow the same structure as theabove file.

10


2.3.2 Phase fractions

This solver will only work for a two phase system. The boundary and initial conditions of eachphase are set in the /0 directory. The files which define these conditions are /0/alpha.gas and/0/alpha.liquid.

The file /0/alpha.gas which defines the gas phase fraction, has a non uniform field which wasgenerated using the setFields utility of OpenFOAM. This will be discussed later in the tutorial. Atthis stage in the tutorial, it is good practice to delete the old /0/alpha.gas file and replace it withthe one below.

FoamFile{

version 2.0;format ascii ;class volScalarField ;location ”0”;object alpha.gas;

}// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

dimensions [0 0 0 0 0 0 0];

internalField uniform 1;

boundaryField{

inlet{

type fixedValue;value uniform 0;

}outlet{

type inletOutlet ;phi phi.gas;inletValue uniform 1;value uniform 1;

}walls{

type zeroGradient;}defaultFaces{

type empty;}

}

The above file has a uniform internal field of 1 for alpha.gas. This can easily be changed later usingthe setFields utility. The inlet value for alpha.gas is set to 1 which means that only gas is enteringthe bubble column. The outlet boundary condition is of type inletOutlet. The zero gradient bound-ary condition is once again used at the wall.

11


The file /0/alpha.liquid for the case will also require replacing with the file below for the samereason as /0/alpha.gas.

FoamFile{

version 2.0;format ascii ;class volScalarField ;location ”0”;object alpha. liquid ;

}// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

dimensions [0 0 0 0 0 0 0];

internalField uniform 0;

boundaryField{

inlet{

type fixedValue;value uniform 0;

}outlet{

type inletOutlet ;phi phi. liquid ;inletValue uniform 0;value uniform 0;

}walls{

type zeroGradient;}defaultFaces{

type empty;}

}

12


2.3.3 Pressure and hydrostatic pressure

The initial and boundary conditions for the pressure and hydrostaticless pressure are defined inthe files /0/p and /0/p_rgh respectively. The file p contains the pressure for the system. Thispressure is used for thermodynamic purposes. However, OpenFOAM does not solve for this pressurein the pressure equation. Instead OpenFOAM solves for the hydrstaticless pressure, p rgh. Thethermodynamic pressure, p, is then calculated after p rgh has been solved using the equation.

p = p rgh+ ρgh (2.1)

The file /0/p is shown below.

1 FoamFile2 {3 version 2.0;4 format ascii ;5 class volScalarField ;6 object p;7 }8 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //9

10 dimensions [1 −1 −2 0 0 0 0];1112 internalField uniform 1e5;1314 boundaryField15 {16 inlet17 {18 type calculated ;19 value $internalField ;20 }21 outlet22 {23 type calculated ;24 value $internalField ;25 }26 walls27 {28 type calculated ;29 value $internalField ;30 }31 }

From the above it is evident that the pressure inside the column is 1e5 Pa. The boundary conditionsare calculated to maintain this pressure within the column at initialisation.

The file /0/p_rgh is shown below.

1 FoamFile2 {3 version 2.0;4 format ascii ;5 class volScalarField ;6 object p rgh;7 }8 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

13


910 dimensions [1 −1 −2 0 0 0 0];1112 internalField uniform 1e5;1314 boundaryField15 {16 inlet17 {18 type fixedFluxPressure;19 value $internalField ;20 }21 outlet22 {23 type prghPressure;24 p $internalField ;25 value $internalField ;26 }27 walls28 {29 type fixedFluxPressure;30 value $internalField ;31 }32 }

The inlet pressure is fixed to the internal field value of 1e5 Pa and the outlet pressure is of typeprghPressure which will calculate the pressure at the outlet without the hydrostatic effects. This isdone through simple manipulation of equation 2.1, yielding the equation below.

p rgh = p− ρgh (2.2)

14


2.3.4 Temperature

The initial and boundary conditions for the temperature of the gas and liquid phases are defined inthe files /0/T.gas and /0/T.liquid, respectively. Below is the file /0/T.gas.

1 FoamFile2 {3 version 2.0;4 format ascii ;5 class volScalarField ;6 object T.gas;7 }8 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //9

10 dimensions [0 0 0 1 0 0 0];1112 internalField uniform 350;1314 boundaryField15 {16 walls17 {18 type zeroGradient;19 }20 outlet21 {22 type inletOutlet ;23 phi phi.gas;24 inletValue $internalField ;25 value $internalField ;26 }27 inlet28 {29 type fixedValue;30 value $internalField ;31 }32 }

The gas phase inside the column is at 350 K at time 0. The inlet gas is also at the same temperatureas the inlet boundary condition is referencing the internalField temperature. For outlet boundarycondition the type inletOutlet is again used along with the zeroGradient boundary condition at thewalls. The file structure of /0/T.liquid is the same as above.

15


2.3.5 Velocity

The initial and boundary conditions for the velocity of the gas and liquid phases are defined in thefiles /0/U.gas and /0/U.liquid respectively. Below is the file /0/U.gas.

1 FoamFile2 {3 version 2.0;4 format binary;5 class volVectorField;6 object U.gas;7 }8 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //9

10 dimensions [0 1 −1 0 0 0 0];1112 internalField uniform (0 0.1 0);1314 boundaryField15 {16 inlet17 {18 type fixedValue;19 value $internalField ;20 }21 outlet22 {23 type pressureInletOutletVelocity ;24 phi phi.gas;25 value $internalField ;26 }27 walls28 {29 type fixedValue;30 value uniform (0 0 0);31 }32 }

From the above code it is evident that the velocity of the gas inside the column and at the inlet is 0.1m/s and that the direction of velocity is in the positive y-direction. The outlet boundary conditionis pressureInletOutletVelocity which will calculate an outlet velocity to satisfy the inlet and internalvelocity and pressure and ensure that momentum and mass are conserved. The file /0/U.liquid

follows the same structure at as above. Verify that the liquid velocity is 0.

16

2.4. DEFINITION OF PHASE PROPERTIES CHAPTER 2. TUTORIAL CASE

2.4 Definition of phase properties

This section will focus on defining the phase system and the phase models for the system. Thisinformation is all defined within the file /constant/phaseProperties. After defining the phases,it then describes how the phases interact with one another and the models to be used for mass andheat transfer.

2.4.1 Definition of phase system and phase models

1 FoamFile2 {3 version 2.0;4 format ascii ;5 class dictionary ;6 location ”constant”;7 object phaseProperties;8 }9 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

1011 type interfaceCompositionPhaseChangeTwoPhaseSystem;1213 phases (gas liquid ) ;1415 gas16 {17 type multiComponentPhaseModel;18 diameterModel isothermal;19 isothermalCoeffs20 {21 d0 3e−3;22 p0 1e5;23 }24 Sc 0.7;2526 residualAlpha 1e−6;27 }2829 liquid30 {31 type multiComponentPhaseModel;32 diameterModel constant;33 constantCoeffs34 {35 d 1e−4;36 }37 Sc 0.7;3839 residualAlpha 1e−6;40 }

The above section of the /constant/phaseProperties file defines the two phase system and thephase models of each phase. The selection of the two phase system is performed in line 11 of the file.It is evident that the ”type” of two phase system is interfaceCompositionPhaseChangeTwoPhas-

17


eSystem. This is one of three available phase system types currently available for the reactingT-woPhaseEulerFoam solver. The three types of two phase systems are described in table 2.2 below.

The phase names are then defined in line 13 of the file. It is evident that in this case thosenames are gas and liquid, respectively. Next, the phase models for each phase must be defined.The phase models will dictate what the phase continuity equation will be. It can be seen on lines17 and 31 that both phases in this system are multi-component phase models. The other availablephase models which can be used within reactingTwoPhaseEulerFoam are outlined in table 2.3 below.

Lines 18-23 and 32-36 are defining the sauter mean diameter for the gas and liquid phases re-spectively. The Schmidt numbers for the gas and liquid phases are defined on lines 24 and 37respectively. The residuals for each phase continuity equation are defined on lines 26 and 39.

Two Phase System DescriptionheatAndMomentumTransferTwoPhaseSystem This system is the most basic system available. It

models momentum and heat transfer in a twoPhas-eSystem. Drag, virtual mass, lift, wall lubricationand turbulent dispersion are all modelled in this twophase system.

interfaceCompositionPhaseChangeTwoPhaseSystem This model adds the effect of mass transfer to thebasic model. The mass transfer between the phasesis calculated according to an interface compositionmodel. The driving force for mass transfer is con-centration gradient.

thermalPhaseChangeTwoPhaseSystem This model adds the effect of mass transfer to the ba-sic model. The mass transfer between the phases iscalculated according to a thermal model. The driv-ing force for mass transfer is a temperature gradient.This model should be used for cases involving evap-oration and condensation.

Table 2.2: Types of two phase systems available in reactingTwoPhaseEulerFoam

Phase Model DescriptionmultiComponentPhaseModel This phase model represents a phase with multiple species.pureIsothermalPhaseModel This model represents a pure phase model for which the temperature

(strictly energy) remains constant.purePhaseModel This model represents a pure phase.reactingPhaseModel This model represents a phase with multiple species and volumetric reactions.

Table 2.3: Types of phase models available in reactingTwoPhaseEulerFoam

18


2.4.2 Blending

Blending is a method used determine the continuous and dispersed phases. As the system becomesmore complex with more phases it becomes difficult to differentiate between the continuous anddispersed phases. However, it is also useful for two phase flow. The ”FullyContinuous” correspondsto the continuous phase and the ”PartlyContinuous” corresponds to the dispersed phase.

1 blending2 {3 default4 {5 type linear ;6 minFullyContinuousAlpha.gas 0.7;7 minPartlyContinuousAlpha.gas 0.5;8 minFullyContinuousAlpha.liquid 0.7;9 minPartlyContinuousAlpha.liquid 0.5;

10 }1112 heatTransferModel13 {14 type linear ;15 minFullyContinuousAlpha.gas 1;16 minPartlyContinuousAlpha.gas 0;17 minFullyContinuousAlpha.liquid 1;18 minPartlyContinuousAlpha.liquid 0;19 }2021 massTransferModel22 {23 type linear ;24 minFullyContinuousAlpha.gas 1;25 minPartlyContinuousAlpha.gas 0;26 minFullyContinuousAlpha.liquid 1;27 minPartlyContinuousAlpha.liquid 0;28 }29 }

The blending factors for the mass transfer and heat transfer models are explicitly described above.Should any other model require a blending coefficient, it will use the coefficients defined in thedefault blending model (line 3). Linear blending methods are to be used for all models which requireit. Other blending methods types include hyperbolic and none.

19


2.4.3 Interface Composition

The interface composition model will describe how the phases interact at the interface. For the cur-rent version of OpenFOAM, only the Saturated model, and Henry model are supported. However,Raoults model and Non Random Two Liquid model exist in the local reactingEulerFoam library,but have not been added to the runtime selectable table as of yet.

1 interfaceComposition2 (3 (gas in liquid )4 {5 type Saturated;6 species ( water );7 Le 1.0;8 saturationPressure9 {

10 type ArdenBuck;11 }12 }1314 ( liquid in gas)15 {16 type Henry;17 species ( air ) ;18 k ( 1.492e−2 );19 Le 1.0;20 }21 ) ;

The above section of the file /constant/phaseProperties describes the interface composition mod-els to be used for a species when it changes phase. The first interface composition model definedwill be examined. It is evident from line 5 above that the saturation model used is of type ”Satu-rated” and the species being transported is ”water”. The saturation pressure is determined usingthe ”ArdenBuck” correlation. Different saturation models can be used to determine the interfacecomposition of a species. These models are outlined in table 2.4 below. The lewis number is theratio of thermal diffusivity to mass diffusivity and in this case it is given a value of 1.0.

The above section of code defines how much water will transfer from the continuous liquid phase tothe dispersed gas phase. The method OpenFOAM uses to evaluate the interface composition willbe further examined later in the report.

20


Saturation Model DescriptionAntoine Uses the Antoine equation to determine vapour pressure in natural log form.

The coefficients to be supplied are A, B and C.Antoine Extended Uses the Antoine equation to determine vapour pressure in natural log form.

The coefficients to be supplied are A, B, C, D and E.ArdenBuck Uses the ArdenBuck correlation to determine the vapour pressure.

This model is only suitable for a water and air combination.constant This model returns a constant saturation temperature and pressure.function1 This model can only be used to determine a saturation temperature

in terms of a saturation pressure.polynomial This model can only be used to determine a saturation temperature

in terms of a saturation pressure.

Table 2.4: Types of saturation models available in reactingTwoPhaseEulerFoam

2.4.4 Heat transfer

The heat transfer model describes the heat transfer between the phases at the interface. The modelcalculates the product of the heat transfer coefficient and the surface area. The heat transfer mod-els currently supported by the reactingEulerFoam solvers are the spherical and RanzMarshall models.

1 heatTransfer.gas2 (3 (gas in liquid )4 {5 type spherical ;6 residualAlpha 1e−4;7 }89 ( liquid in gas)

10 {11 type RanzMarshall;12 residualAlpha 1e−4;13 }14 ) ;1516 heatTransfer. liquid17 (18 (gas in liquid )19 {20 type RanzMarshall;21 residualAlpha 1e−4;22 }2324 ( liquid in gas)25 {26 type spherical ;27 residualAlpha 1e−4;28 }29 ) ;

The heat transfer needs to be defined for both phases. This is evident in lines 1 and 16 of the code.

21


The first section of code will be evaluated (lines 1 - 14). This defines the heat transfer model for thegas phase. Heat transfer of the gas phase can occur in two different situations. It can occur whenthe gas is the dispersed phase (line 3) or when the gas is the continuous phase (line 9). The heattransfer model to be used in each situation are defined in lines 5 and 11. The same analysis can beperformed on the heat transfer model for the liquid phase.

2.4.5 Mass transfer

The mass transfer model will describe the mass transfer between the phases at the interface. Themodel calculates the product of the mass transfer coefficient and the surface area. The mass trans-fer models currently supported by the reactingEulerFoam solvers are the sperical model and theFrossling model.

1 massTransfer.gas2 (3 (gas in liquid )4 {5 type spherical ;6 Le 1.0;7 }89 ( liquid in gas)

10 {11 type Frossling ;12 Le 1.0;13 }14 ) ;1516 massTransfer.liquid17 (18 (gas in liquid )19 {20 type Frossling ;21 Le 1.0;22 }2324 ( liquid in gas)25 {26 type spherical ;27 Le 1.0;28 }29 ) ;

The mass transfer within the liquid and gas phases are defined in a similar manner to the heat trans-fer. That is it is explicitly defined for situations in which each phase is continuous and dispersed.

The mass transfer model for the gas phase will be discussed (lines 1-14). The mass transfer modelused to define the gas when it is the dispersed phase (line 3), is the spherical mass transfer model(lines 5). However, when the gas is the continuous phase, the Frossling model (line 11) is usedto calculate the mass transfer coefficient. The Lewis number is the ratio of thermal diffusivity tomass diffusivity and is given a value of 1.0 in the mass transfer model. This Le number is used inthe calculation of the mass transfer coefficient. The same approach is used to determine the masstransfer model for the liquid phase.

22


2.4.6 Surface tension and aspect ratio

The surface tension model describes the surface tension at the interface. The solver currently onlysupports a constant surface tension model. The aspect ratio is refering to the bubble aspect ratio,which will describe the shape of the bubble. A number of aspect ratio models are supported by thereactingEulerFoam solvers. These include, the constant model, the Tomiyama model, the Vakhru-shev Efremov model and the Wellek model.

1 surfaceTension2 (3 (gas and liquid)4 {5 type constant;6 sigma 0.07;7 }8 ) ;9

10 aspectRatio11 (12 (gas in liquid )13 {14 type constant;15 E0 1.0;16 }1718 ( liquid in gas)19 {20 type constant;21 E0 1.0;22 }23 ) ;

It should be noted that the surface tension model is valid for a phase pair. It evident from theabove file that the phase pair is gas and liquid (line 3). The surface tension model used is of typeconstant (line 5). This is the only surface tension model supported by reactingTwoPhaseEulerFoam.The value for surface tension is 0.07 N/m. The model used to describe the aspect ratio is of typeconstant for the situations described on (lines 14 and 20).

23


2.4.7 Drag and virtual mass

The drag model describes the drag effects the phases impart onto one another. The model calculatesthe drag coefficients for each phase when it is continuous. The virtual mass model describes theinertial effects the phases have on one another. The model calculates the virtual mass coefficientsfor each phase.

1 drag2 (3 (gas in liquid )4 {5 type SchillerNaumann;6 residualRe 1e−3;7 swarmCorrection8 {9 type none;

10 }11 }1213 ( liquid in gas)14 {15 type SchillerNaumann;16 residualRe 1e−3;17 swarmCorrection18 {19 type none;20 }21 }22 ) ;2324 virtualMass25 (26 (gas in liquid )27 {28 type constantCoefficient ;29 Cvm 0.5;30 }3132 ( liquid in gas)33 {34 type constantCoefficient ;35 Cvm 0.5;36 }37 ) ;

The drag model requires defining when the liquid phase is the continuous phase and the gas phaseis dispersed (line 2) and when the phases are reversed (line 13). The drag model is defined on lines5 and 15. In this case, the SchillerNaumann model is defined for both conditions.

The virtual mass model also requires defining for both phase conditions (lines 26 and 32). TheconstantCoefficient model is used in this case and the virtual mass coefficient is set to 0.5.

24

2.5. DEFINITION OF THERMOPHYSICAL PROPERTIES CHAPTER 2. TUTORIAL CASE

2.5 Definition of thermophysical properties

This section will focus on defining the properties of the species within the individual phases. Thisinformation is all defined in the files /constant/thermophysicalProperties.gas and/constant/thermophysicalProperties. Readers should consult the documentation on thermo-physical models in the OpenFOAM user-guide if any further explanation is required.

2.5.1 Thermodynamic properties of the phase

The thermodynamic properties of the gas phase is defined in the first section of the file/constant/thermophysicalProperties.gas below.

1 FoamFile2 {3 version 2.0;4 format ascii ;5 class dictionary ;6 location ”constant”;7 object thermophysicalProperties.gas;8 }9 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

1011 thermoType12 {13 type heRhoThermo;14 mixture multiComponentMixture;15 transport const;16 thermo hConst;17 equationOfState perfectGas;18 specie specie ;19 energy sensibleInternalEnergy;20 }2122 dpdt yes;

The thermoType model specifies the complete thermophysical model used to describe the system(line 11). It can be seen from (line 19) that the internal energy equation is used for the system. Thetype model used for the gas phase is heRhoThermo (line 13). This will set up the model calculatiointo be based on internal energy and density. The gas phase is defined as a multiComponentMixture(line 14) with constant transport properties with respect to temperature (line 15). The hConstthermo model is selected in (line 16 ) which assumes the specific heat capacity of the gas remainsconstant in the evaluation of the enthalpy of the gas phase. The gas phase is then described as aperfect gas (line 17) and with different species components (line 18). The purpose of (line 22) is toinclude the pressure term in the energy equation.

25

2.5. DEFINITION OF THERMOPHYSICAL PROPERTIES CHAPTER 2. TUTORIAL CASE

2.5.2 Species definition within the phase

The file /constant/thermophysicalProperties.gas then continues to define the species compo-nents within the gas phase and their properties. It should be noted the variables supplied in thissection will depend on the thermoType selections made in the previous subsection 2.5.1.

1 species2 (3 air4 water5 ) ;67 inertSpecie air ;89 ”(mixture|air)”

10 {11 specie12 {13 molWeight 28.9;14 }15 thermodynamics16 {17 Hf 0;18 Cp 1012.5;19 }20 transport21 {22 mu 1.84e−05;23 Pr 0.7;24 }25 }2627 water28 {29 specie30 {31 molWeight 18.0153;32 }33 thermodynamics34 {35 Hf −1.3435e+07;36 Cp 1857.8;37 }38 transport39 {40 mu 1.84e−05;41 Pr 0.7;42 }43 }

It is evident from lines (1-5) that the species components of the gas phase are air and water. Thespecies ”air” is then defined as inert (line 7). The mixture is then defined and and the propertiesof each component in the gas phase is defined. The molecular weight is to be supplied in unitsof kg/kmol (lines 13 and 31). As a result of selecting the hConst thermo model, the specific heatcapacity, cp, and heat of formation Hf require defining (lines 17, 18, 35 and 36). The units are

26

2.6. SYSTEM SET-UP CHAPTER 2. TUTORIAL CASE

J/kg.K and J/kg respectively. It should be noted that condition the heats of formation is evaluatedat is 25 C and 1 atm. The enthalpy can then be computed at any temperature using the equationbelow.

Hf(T ) = Hf(25 oC) + cp(T − 25) (2.3)

Finally the transport variables require defining (lines 22, 23, 40 and 41). The first is the dynamicviscosity, µ, which has units Pa.s. The second is the dimentionless Prandtl number which describesthe ratio of momentum diffusivity to thermal diffusivity.

2.6 System set-up

This section will focus on the files in the /system/ directory. This directory contains dictionariesto control mesh settings and solver settings. The table below outlines the files in this directory.

File name File descriptionblockMeshDict Dictionary which contains instructions on how to generate the mesh structure.controlDict Dictionary which contains the run control parameters for the solution procedure.fvSchemes Dictionary which contains the discretization schemes used in the solution.

This dictionary is run-time selectable.fvSolution Dictionary where the equation solvers, tolerances and other algorithm controls

are set.setFieldsDict Dictionary which contains instructions on generating a non uniform initial

conditions in a case.

Table 2.5: Description of files in the system directory

The file /system/setFieldsDict will be examined below.

1 FoamFile2 {3 version 2.0;4 format ascii ;5 class dictionary ;6 location ”system”;7 object setFieldsDict ;8 }9 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

1011 defaultFieldValues12 (13 volScalarFieldValue alpha.gas 114 volScalarFieldValue alpha. liquid 015 ) ;1617 regions18 (19 boxToCell20 {21 box (0 0 0) (0.15 0.501 0.1) ;22 fieldValues23 (24 volScalarFieldValue alpha.gas 025 volScalarFieldValue alpha. liquid 1

27

2.7. RUN THE CASE AND VISUALIZE IN PARAVIEW CHAPTER 2. TUTORIAL CASE

26 ) ;27 }28 ) ;

The objective of the setFields utility for this tutorial is to add liquid to the column. In section 2.3.2the boundary and initial conditions were set up to contain no water in the system. The setFieldsDictis informed of this fact in (lines 11 - 15). The utility is then informed that a ”region” (line 17) oftype boxToCell (line 19) requires changing. The bottom left and top right points of the rectangularregion are then defined (line 21). The new field values within the region are then defined (lines 24and 25).

2.7 Run the case and visualize in Paraview

The case is nearly ready to run. It is good practice to rename the original 0/ directory before startingwith a case because the setFields utility will change the initial conditions.

cp −rf 0 0orig

The simulation usually takes some time to run completely. In order to decrease execution time ofthe case the end time of the case should be changed from 100 to 10 and the write interval should bechanged from 1 to 0.1. These changes are made in the system/controlDict file.

Then generate the mesh using the blockMesh utilty.

blockMesh

The liquid phase must be added to the initial conditions using the setFields utility.

setFields

Finally the solver can be run on the case, sending the output to a log file.

reactingTwoPhaseEulerFoam >& log&

Open the case in paraview.

paraFoam

It is possible to see the water transferring from the liquid to the gas phase in paraview. To dothis select water.gas from the fields tab in the properties section. Click apply. The water.gas fieldthen needs to be selected in the main drop down menu above the viewing window. Press play andwatch the mass transfer. Figure 2.2 is a screenshot of the bubble column at the final timestep. Theconcentration distribution of water in the gas phase across the column is illustrated. Notice howthe gas is saturated with water as it passes through the liquid. Figure 2.3 shows the temperaturedistribution across the column at the final time-step. The gas entering the column is at the sametemperature as the liquid in the column, however, there is a clear temperature distribution. This isas a result of water transferring phase. The water is transferring from the liquid to the gas phasewhich requires energy. The energy expended is in the form of heat energy and heat transfer is clearlyhappening at the interface between the two phases.

28

2.7. RUN THE CASE AND VISUALIZE IN PARAVIEW CHAPTER 2. TUTORIAL CASE

Figure 2.2: Concentration of water in the gas phase at the final timestep

Figure 2.3: Temperature distribution accross column at the final timestep

29

Chapter 3

Classes

At this point the reader should have an understanding on the general theory employed by the re-actingTwoPhaseEulerFoam solver and how to apply the solver to a case. This section will focus onclasses which appear in the reactingTwoPhaseEulerFoam solver. The important classes and files forthis solver are located in the directory below. All files mentioned in this chapter will be in referenceto this directory.$FOAM_SOLVERS/multiphase/reactingEulerFoam/reactingTwoPhaseEulerFoam

The main application file for reactingTwoPhaseEulerFoam is located inreactingTwoPhaseEulerFoam.C.

The application starts by declaring the header files required to perform the finite volume calcu-lations and PIMPLE algorithm.

1 #include ”fvCFD.H”2 #include ”twoPhaseSystem.H”3 #include ”phaseCompressibleTurbulenceModel.H”4 #include ”pimpleControl.H”5 #include ”localEulerDdtScheme.H”6 #include ”fvcSmooth.H”

It is assumed that the reader already has an understanding of finite volume analysis in OpenFOAMand the PIMPLE procedure for two-phase flows. A good explanation of the PIMPLE procedure fortwo-phase flow and the MULES procedure used to solve the phase continuity equation is providedby Manni (2014). The focus of this report is how OpenFOAM calculates the mass and heat transferat the interface.

30

3.1. TWOPHASESYSTEM CLASS CHAPTER 3. CLASSES

3.1 twoPhaseSystem class

The two phase system class is responsible for the heat and mass transfer at the interface. The headerfile twoPhaseSystem.H is located in the directory twoPhaseSystem/.

3.1.1 twoPhaseSystem.H

1 #ifndef twoPhaseSystem H2 #define twoPhaseSystem H34 #include ”phaseSystem.H”56 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //78 namespace Foam9 {

1011 class dragModel;12 class virtualMassModel;

The file starts by declaring phaseSystem.H and forward declaring the dragModel and virtualMass-Model classes.

1 class twoPhaseSystem2 :3 public phaseSystem

The twoPhaseSystem class exhibits inheritance from the phaseSystem class.

1 protected:23 // Protected data45 //− Phase model 16 phaseModel& phase1 ;78 //− Phase model 29 phaseModel& phase2 ;

The phases are protected data and are of type phaseModel.

1 // Selectors23 static autoPtr<twoPhaseSystem> New4 (5 const fvMesh& mesh6 ) ;

The selector ”New” is declared. This static function is used to create the two-phase system in thecase and will be explained in section 3.1.4.

1 {2 public :3

31


4 //− Runtime type information5 TypeName(”twoPhaseSystem”);67 // Declare runtime construction89 declareRunTimeSelectionTable

10 (11 autoPtr,12 twoPhaseSystem,13 dictionary ,14 (15 const fvMesh& mesh16 ) ,17 (mesh)18 ) ;

A runtime construction is created allowing the type of twoPhaseSystem to be selected by the userat runtime in the case set up. The procedure behind the generation of this runtime selection tableis outlined in section 3.1.3.

1 //− Return the momentum transfer matrices2 virtual autoPtr<momentumTransferTable> momentumTransfer() const = 0;34 //− Return the heat transfer matrices5 virtual autoPtr<heatTransferTable> heatTransfer() const = 0;67 //− Return the mass transfer matrices8 virtual autoPtr<massTransferTable> massTransfer() const = 0;9

10 //− Return true if there is mass transfer11 bool transfersMass() const;1213 //− Return the interfacial mass flow rate14 tmp<volScalarField> dmdt() const;1516 //− Solve for the phase fractions17 virtual void solve () ;

Important member functions of the twoPhaseSystem class are declared above. The first three func-tions momentumTransfer, heatTransfer and MassTransfer (lines 2, 5 and 8) are virtual functionswhich will be called by reactingTwoPhaseEulerFoam and return pointers to matrices. They appearin the momentum, heat and mass conservation equations respectively. On (line 11) a boolean switchcalled transferMass is declared which is used to determine if mass transfer will occur in the system.The solve function declared on (line 17) is used to solve the continuity equation. It will be examinedin section 3.1.2.

32


3.1.2 twoPhaseSystem.C

1 #include ”twoPhaseSystem.H”2 #include ”dragModel.H”3 #include ”virtualMassModel.H”45 #include ”MULES.H”6 #include ”subCycle.H”78 #include ”fvcDdt.H”9 #include ”fvcDiv.H”

10 #include ”fvcSnGrad.H”11 #include ”fvcFlux.H”12 #include ”fvcSup.H”1314 #include ”fvmDdt.H”15 #include ”fvmLaplacian.H”16 #include ”fvmSup.H”

The header files to be used in twoPhaseSystem.C are listed above. The drag and virtualMass modelswere declared in section 3.1.1 and their header files are now included in twoPhaseSystem.C (lines 2and 3). It is evident that the MULES procedure will be employed in this file (line 5) and that finitevolume calculations will be performed (lines 8 - 16).

1 Foam::twoPhaseSystem::twoPhaseSystem2 (3 const fvMesh& mesh4 )5 :6 phaseSystem(mesh),7 phase1 (phaseModels [0]),8 phase2 (phaseModels [1])9 {

10 phase2 .volScalarField :: operator=(scalar(1) − phase1 );1112 volScalarField& alpha1 = phase1 ;13 mesh.setFluxRequired(alpha1.name());14 }

The twoPhaseSystem constructor is then defined. It is evident from (line 3) that the two-phasesystem takes the object mesh as an argument. phaseSystem is the parent class which is initializedwith the argument mesh (line 6). The object phase1 is initialized with the first argument of thephaseModels object (line 7) and phase2 is initialized with the second argument of the phaseModelsobject (line 8). It is evident from (line 10) that phase2 is calculated using the equation.

α2 = 1− α1 (3.1)

1 void Foam::twoPhaseSystem::solve()2 {3 const Time& runTime = mesh .time();45 volScalarField& alpha1 = phase1 ;6 volScalarField& alpha2 = phase2 ;

33


The solve function is defined in twoPhaseSystem.C and is used to solve the phase continuity equa-tion 1.4. It is a convoluted function which will not be analysed in detail. The OF course report ofManni (2014), should be consulted for a detailed description of how the solver employs the MULESalgorithm to solve the phase continuity equation.

1 MULES::explicitSolve2 (3 geometricOneField(),4 alpha1,5 phi ,6 alphaPhi1,7 Sp,8 Su,9 phase1 .alphaMax(),

10 011 ) ;

It is evident from the above section of the solve function, that the MULES algorithm is employedto solve for α1.

1 Info<< alpha1.name() << ” volume fraction = ”2 << alpha1.weightedAverage(mesh .V()).value()3 << ” Min(alpha1) = ” << min(alpha1).value()4 << ” Max(alpha1) = ” << max(alpha1).value()5 << endl;67 // Ensure the phase−fractions are bounded8 alpha1.maxMin(0, 1);9

10 // Update the phase−fraction of the other phase11 alpha2 = scalar(1) − alpha1;12 }13 }

The solve function ends by outputting the values calculated for α1. Boundedness of α1 is thenverified and finally α2 is calculated using equation 3.1.

34


3.1.3 twoPhaseSystems.C

1 #include ”addToRunTimeSelectionTable.H”23 #include ”phaseSystem.H”4 #include ”twoPhaseSystem.H”5 #include ”MomentumTransferPhaseSystem.H”6 #include ”HeatTransferPhaseSystem.H”7 #include ”InterfaceCompositionPhaseChangePhaseSystem.H”8 #include ”ThermalPhaseChangePhaseSystem.H”

The declaration files of the two-phase systems available are on lines 5-8. It is evident that the phasesystems described are MomentumTransferPhaseSystem, HeatTransferPhaseSystem, InterfaceCom-positionPhaseChangePhaseSystem and ThermalPhaseChangePhaseSystem.

1 namespace Foam2 {3 typedef4 HeatTransferPhaseSystem5 <6 MomentumTransferPhaseSystem<twoPhaseSystem>7 >8 heatAndMomentumTransferTwoPhaseSystem;9

10 addNamedToRunTimeSelectionTable11 (12 twoPhaseSystem,13 heatAndMomentumTransferTwoPhaseSystem,14 dictionary ,15 heatAndMomentumTransferTwoPhaseSystem16 ) ;1718 typedef19 InterfaceCompositionPhaseChangePhaseSystem20 <21 MomentumTransferPhaseSystem<twoPhaseSystem>22 >23 interfaceCompositionPhaseChangeTwoPhaseSystem;2425 addNamedToRunTimeSelectionTable26 (27 twoPhaseSystem,28 interfaceCompositionPhaseChangeTwoPhaseSystem,29 dictionary ,30 interfaceCompositionPhaseChangeTwoPhaseSystem31 ) ;3233 typedef34 ThermalPhaseChangePhaseSystem35 <36 MomentumTransferPhaseSystem<twoPhaseSystem>37 >38 thermalPhaseChangeTwoPhaseSystem;3940 addNamedToRunTimeSelectionTable

35


41 (42 twoPhaseSystem,43 thermalPhaseChangeTwoPhaseSystem,44 dictionary ,45 thermalPhaseChangeTwoPhaseSystem46 ) ;47 }

The phase systems require input arguments and are layered in a manner which is not user friendly.Type definitions are used to simplify the process of inputting a two-phase system at runtime.

The interfaceCompositionPhaseChangeTwoPhaseSystem typedef will be analysed. This is type-def in which the twoPhaseSystem class is an argument of the MomentumTransferPhaseSystem (line21). This is then passed as an argument to the InterfaceCompositionPhaseChangePhaseSystem(line 19). The two-phase system created is then passed to a runtime selection table for the twoPhasesystem (lines 25 - 31).

It should be noted that the MomentumTransferPhaseSystem is present in all the two-phase sys-tems in reactingTwoPhaseEulerFoam. This is because it is the system which solves the momentumequations. Note that the two-phase systems created in the above file are the ones described in table2.2.

36


3.1.4 newTwoPhaseSystem.C

The file below contains the definition of static function used to select the two-phase system.

1 #include ”twoPhaseSystem.H”23 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Selector ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //45 Foam::autoPtr<Foam::twoPhaseSystem> Foam::twoPhaseSystem::New6 (7 const fvMesh& mesh8 )9 {

10 const word systemType11 (12 IOdictionary13 (14 IOobject15 (16 propertiesName,17 mesh.time().constant(),18 mesh,19 IOobject::MUST READ IF MODIFIED,20 IOobject::NO WRITE,21 false22 )23 ) .lookup(”type”)24 ) ;25 Info<< ”Selecting twoPhaseSystem ” << systemType << endl;2627 auto cstrIter = dictionaryConstructorTablePtr −>cfind(systemType);2829 if (! cstrIter .found())30 {31 FatalErrorInFunction32 << ”Unknown twoPhaseSystem type ”33 << systemType << nl << nl34 << ”Valid twoPhaseSystem types :” << endl35 << dictionaryConstructorTablePtr −>sortedToc()36 << exit(FatalError);37 }3839 return cstrIter ()(mesh);40 }

The header file twoPhaseSystem.H is declared on line 1 because this is where the declaration of the”New” selector is located. It can be seen that the mesh argument is passed to the function on line7 of the file. The two phase system is then read from the propertiesName dictionary (line 16). Thetype of two-phase system is found by searching for word ”type” in the dictionary (line 23). Thesystem defined in the propertiesName dictionary is assigned the variable name ”systemType” (line10).The function then searches for ”systemType” from the runtime selection table created in section3.1.3. If the ”systemType” is not in the table it returns the error described in (lines 31-36). Otherwisethe systemType is returned with the object mesh as an argument (line 30).

37

3.2. PHASEMODEL CLASS CHAPTER 3. CLASSES

3.2 phaseModel class

The phases in the two-phase system were objects of the class phaseModel. The files which constructthe phaseModel class are located in the directory ../phaseSystems/phaseModel/phaseModel/.Note that the directory phaseSystems is located in the directory reactingEulerFoam. This direc-tory contains classes which are templated and are also used in the reactingMultiphaseEulerFoam

solver. The classes are created in such a way that they work for an unlimited number of phases.This class will contain the momentum and species fraction equations derived in chapter 1.

3.2.1 phaseModel.H

1 #include ”dictionary.H”2 #include ”dimensionedScalar.H”3 #include ”volFields.H”4 #include ”surfaceFields.H”5 #include ”fvMatricesFwd.H”6 #include ”rhoThermo.H”7 #include ”phaseCompressibleTurbulenceModelFwd.H”8 #include ”runTimeSelectionTables.H”

The header files to be used by the phaseModel class are declared. Notice the rhoThermo.H headerfile.

1 namespace Foam2 {34 class phaseSystem;5 class diameterModel;

The forward declaration of phaseSystem and diameterModel classes.

1 class phaseModel2 :3 public volScalarField4 {5 // Private data67 //− Reference to the phaseSystem to which this phase belongs8 const phaseSystem& fluid ;9

10 //− Name of phase11 word name ;1213 //− Index of phase14 label index ;

The phaseModel class is inherited from the volScalarField class (line 3). An object called fluid isdeclared and it is of the class phaseSystem. The name of the phase is also declared (line 11) and isgiven an index (line 14).

1 // Declare runtime construction23 declareRunTimeSelectionTable4 (

38


5 autoPtr,6 phaseModel,7 phaseSystem,8 (9 const phaseSystem& fluid,

10 const word& phaseName,11 const label index12 ) ,13 ( fluid , phaseName, index)14 ) ;

A runtime construction is declared allowing the user to select the phase model for each phase inthe case set up. The procedure behind the generation of this runtime selection table is outlined insection 3.2.3.

1 static autoPtr<phaseModel> New2 (3 const phaseSystem& fluid,4 const word& phaseName,5 const label index6 ) ;

The selector ”New” is declared. This static function is used to create the phaseModels in the caseand is explained in section 3.2.4.

1 //− Return the momentum equation2 virtual tmp<fvVectorMatrix> UEqn() = 0;34 //− Return the enthalpy equation5 virtual tmp<fvScalarMatrix> heEqn() = 0;67 //− Return the species fraction equation8 virtual tmp<fvScalarMatrix> YiEqn(volScalarField& Yi) = 0;

The following virtual member functions refer to the momentum, enthalpy and species fraction equa-tions without momentum transfer, heat transfer and mass transfer respectively between the phases.

39


3.2.2 phaseModel.C

1 Foam::phaseModel::phaseModel2 (3 const phaseSystem& fluid,4 const word& phaseName,5 const label index6 )7 :8 volScalarField9 (

10 IOobject11 (12 IOobject::groupName(”alpha”, phaseName),13 fluid .mesh().time().timeName(),14 fluid .mesh(),15 IOobject::READ IF PRESENT,16 IOobject::AUTO WRITE17 ) ,18 fluid .mesh(),19 dimensionedScalar(dimless, Zero)20 ) ,2122 fluid ( fluid ) ,23 name (phaseName),24 index (index),

The constructor of the class phaseModel is defined in the file phaseModel.C. The arguments fluid,phaseName and index are passed to the phaseModel class during construction (lines 3-5). The parentclass volVectorVield is then constructed using ”alpha.phaseName” as the scalar (line 12). The classmember data, fluid, name and index are then initialized with the arguments passed to the classduring construction. (lines 22-24).

40


3.2.3 phaseModels.C

1 #include ”addToRunTimeSelectionTable.H”23 #include ”rhoThermo.H”4 #include ”rhoReactionThermo.H”56 #include ”CombustionModel.H”78 #include ”phaseModel.H”9 #include ”ThermoPhaseModel.H”

10 #include ”IsothermalPhaseModel.H”11 #include ”AnisothermalPhaseModel.H”12 #include ”PurePhaseModel.H”13 #include ”MultiComponentPhaseModel.H”14 #include ”InertPhaseModel.H”15 #include ”ReactingPhaseModel.H”16 #include ”MovingPhaseModel.H”

The declaration files of partial phase models are available are on lines (9-16). rhoThermo.H, rhoRe-actionThermo.H and CombustionModel.H are the declaration files of classes which describe thethermodynamics of the individual phase. The classes declared above are combined in such a way togenerate a complete phase model.

1 namespace Foam2 {3 typedef4 AnisothermalPhaseModel5 <6 PurePhaseModel7 <8 InertPhaseModel9 <

10 MovingPhaseModel11 <12 ThermoPhaseModel<phaseModel, rhoThermo>13 >14 >15 >16 >17 purePhaseModel;1819 addNamedToRunTimeSelectionTable20 (21 phaseModel,22 purePhaseModel,23 phaseSystem,24 purePhaseModel25 ) ;26 typedef27 IsothermalPhaseModel28 <29 PurePhaseModel30 <31 InertPhaseModel

41


32 <33 MovingPhaseModel34 <35 ThermoPhaseModel<phaseModel, rhoThermo>36 >37 >38 >39 >40 pureIsothermalPhaseModel;4142 addNamedToRunTimeSelectionTable43 (44 phaseModel,45 pureIsothermalPhaseModel,46 phaseSystem,47 pureIsothermalPhaseModel48 ) ;4950 typedef51 AnisothermalPhaseModel52 <53 MultiComponentPhaseModel54 <55 InertPhaseModel56 <57 MovingPhaseModel58 <59 ThermoPhaseModel<phaseModel, rhoReactionThermo>60 >61 >62 >63 >64 multiComponentPhaseModel;6566 addNamedToRunTimeSelectionTable67 (68 phaseModel,69 multiComponentPhaseModel,70 phaseSystem,71 multiComponentPhaseModel72 ) ;73 typedef74 AnisothermalPhaseModel75 <76 MultiComponentPhaseModel77 <78 ReactingPhaseModel79 <80 MovingPhaseModel81 <82 ThermoPhaseModel<phaseModel, rhoReactionThermo>83 >,84 CombustionModel<rhoReactionThermo>85 >

42


86 >87 >88 reactingPhaseModel;8990 addNamedToRunTimeSelectionTable91 (92 phaseModel,93 reactingPhaseModel,94 phaseSystem,95 reactingPhaseModel96 ) ;97 }

Similiarly to the twoPhaseSystems, the phaseModels require type definitions to simplify the processof inputting a phase model at runtime.

The reactingPhaseModel typedef will be analysed as it is the most complicated(line 88). This isthe typedef in which the ThermoPhaseModel has phaseModel, and rhoReactionThermo as the inputarguments. This model is then used as the input argument to the MovingPhaseModel. This modelis then input as one of the two argument to the ReactingPhaseModel. The other argument requiredfor the ReactingPhaseModel is the CombustionModel. The reactingPhaseModel is then used as theinput argument to the MultiComponentPhaseModel. Finally this model is the input argument tothe AnisothermalPhaseModel. The name given to this convoluted typedef is reactingPhaseModelwhich is then added to the runtime selection table (line 90).

Note that the phase model typedefs created in the above file are the ones described in table 2.3.

43


3.2.4 newPhaseModel.C

1 Foam::autoPtr<Foam::phaseModel> Foam::phaseModel::New2 (3 const phaseSystem& fluid,4 const word& phaseName,5 const label index6 )7 {8 const word modelType(fluid.subDict(phaseName).lookup(”type”));9

10 Info<< ”Selecting phaseModel for ”11 << phaseName << ”: ” << modelType << endl;1213 auto cstrIter = phaseSystemConstructorTablePtr −>cfind(modelType);1415 if (! cstrIter .found())16 {17 FatalErrorInFunction18 << ”Unknown phaseModel type ”19 << modelType << nl << nl20 << ”Valid phaseModel types :” << endl21 << phaseSystemConstructorTablePtr −>sortedToc()22 << exit(FatalError);23 }2425 return cstrIter ()( fluid , phaseName, index);26 }

The phase model selector ”New” takes three arguments, fluid which is an phaseSystem object (line3), phaseName (line 4) and index (line 5). The phaseModel is selected by searching the word, ”type”in the subdictionary of the phase system. This is then assigned the variable name modelType (line8). The function then searches for the modelType in the runtime selectable table created in section3.2.3. If the modelType is not found the function will output and error (lines 17-22), otherwise thefunction will return the phaseModel with the fluid, phaseName and index arguments passed to it.

44

3.3. INTERFACECOMPOSITIONPHASECHANGEPHASESYSTEM CHAPTER 3. CLASSES

3.3 InterfaceCompositionPhaseChangePhaseSystem

This class is responsible for calculating the amount of mass transfer occuring in the system. Theinterface temperature will also vary as a result. The functions employed to determine the masstransfer and interface temperatures are massTransfer and correctThermo respectively.

3.3.1 InterfaceCompositionPhaseChangePhaseSystem.H

1 #include ”HeatAndMassTransferPhaseSystem.H”23 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //45 namespace Foam6 {78 class interfaceCompositionModel;9

10 /∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗\11 Class InterfaceCompositionPhaseChangePhaseSystem Declaration12 \∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗/1314 template<class BasePhaseSystem>15 class InterfaceCompositionPhaseChangePhaseSystem16 :17 public HeatAndMassTransferPhaseSystem<BasePhaseSystem>18 {

It is evident from the declaration of the interfaceCompositionPhaseChangePhaseSystem class thatthe class exhibits inheritance from the HeatAndMassTransferPhaseSystem class (line 17). There isa forward declaration of the class interfaceCompositionModel on line 8. This class contains all themodels to evaluate the properties at the interface.

1 protected:23 // Protected typedefs45 typedef HashTable6 <7 autoPtr<interfaceCompositionModel>,8 phasePairKey,9 phasePairKey::hash

10 > interfaceCompositionModelTable;111213 // Protected data1415 // Sub Models1617 //− Interface composition models18 interfaceCompositionModelTable interfaceCompositionModels ;

A hash table typedef called interfaceCompositionModelTable (line 10) is then created for the interfacecomposition models. The object interfaceCompositionModels is then created from the typedef classinterfaceCompositionModelTable (line 18). This object will contain all the interfaceCompositionmodels for the system.

45


3.3.2 InterfaceCompositionPhaseChangePhaseSystem.C

1 #include ”InterfaceCompositionPhaseChangePhaseSystem.H”2 #include ”interfaceCompositionModel.H”345 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Constructors ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //67 template<class BasePhaseSystem>8 Foam::InterfaceCompositionPhaseChangePhaseSystem<BasePhaseSystem>::9 InterfaceCompositionPhaseChangePhaseSystem

10 (11 const fvMesh& mesh12 )13 :14 HeatAndMassTransferPhaseSystem<BasePhaseSystem>(mesh)15 {16 this−>generatePairsAndSubModels17 (18 ”interfaceComposition”,19 interfaceCompositionModels20 ) ;21 }

This file opens up with two declaration files. Those are the declaration file for InterfaceComposi-tionPhaseChangePhaseSystem (line 1) and the declaration file for interfaceCompositionModels (line2).

The constructor for the InterfaceCompositionPhaseChangePhaseSystem is then defined. This classis templated for a ”BasePhaseSystem” (line 7), which is amtwoPhaseSystem for this report. Theclass requires the mesh object as an argument. The parent class, HeatAndMassTransferPhaseSys-tem is also construced with argument mesh (line 14). The interfaceCompositionModels object isinitialised using the generatePairsAndSubModels function. This function is declared and defined inphaseSystems/phaseSystem/phaseSystem.H.

Two important functions are located in this file. This first function is massTransfer() which will bedescribed in 3.3.2, and the second is correctThermo() which will be described in 3.3.2.

46


MassTransfer Function

1 template<class BasePhaseSystem>2 Foam::autoPtr<Foam::phaseSystem::massTransferTable>3 Foam::InterfaceCompositionPhaseChangePhaseSystem<BasePhaseSystem>::4 massTransfer() const5 {6 // Create a mass transfer matrix for each species of each phase7 auto eqnsPtr = autoPtr<phaseSystem::massTransferTable>::New();8 auto& eqns = ∗eqnsPtr;9

10 for (const phaseModel& phase : this−>phaseModels )11 {12 const PtrList<volScalarField>& Yi = phase.Y();1314 forAll (Yi, i )15 {16 eqns.set17 (18 Yi[ i ]. name(),19 new fvScalarMatrix(Yi[i], dimMass/dimTime)20 ) ;21 }22 }

The above section of the mass transfer function creates a new mass transfer matrix for each speciesof each phase. The ”New” function belonging to the class autoPtr creates an empty mass transfermatrix. The class autoPtr uses the template massTransferTable which is a typedef of a HashP-trTable defined in the file /phaseSystems/phaseSystem/phaseSystem.H. The pointer value is thenassigned to the variable eqns.

The for loop (line 10) is where the species for each phase is generated. The function will lookthrough all of the phaseModels in the phase object. For this case there are two phases in the phaseobject. The first line in the for loop (line 12) determines which species are in current phase in theloop and stores them in the volScalarField Yi. The nested forAll loop will then create a new volumescalar matrix within the eqns matrix for each component in the phase. The species mass fraction isdefined as the unknown quantity in the matrix (line 18). This matrix represents the mass transferof this component in the phase. This is evident because of units used on line 19.

1 // Sum up the contribution from each interface composition model2 forAllConstIters3 (4 interfaceCompositionModels ,5 interfaceCompositionModelIter6 )7 {8 const phasePair& pair =9 ∗(this−>phasePairs [interfaceCompositionModelIter.key()]);

1011 const interfaceCompositionModel& compositionModel =12 ∗(interfaceCompositionModelIter.object());1314 const phaseModel& phase = pair.phase1();15 const phaseModel& otherPhase = pair.phase2();

47


16 const phasePairKey key(phase.name(), otherPhase.name());1718 const volScalarField& Tf(∗this−>Tf [key]);1920 volScalarField& dmdtExplicit(∗this−>dmdtExplicit [key]);21 volScalarField& dmdt(∗this−>dmdt [key]);2223 scalar dmdtSign(Pair<word>::compare(this−>dmdt .find(key).key(), key));2425 const volScalarField K26 (27 this−>massTransferModels [key][phase.name()]−>K()28 ) ;

The effect of mass transfer is then evaluated for every composition model in the system. In the caseof the two phase system described in section 2. The interface composition models were ”Saturated”for when the gas was present in the liquid, and ”Henry” for when the liquid was present in the gas(line 1). The Saturation model will be explored.

Line 18 defines the interface temperature, which is crucial information as mass transfer is tem-perature dependent. dmdtExplicit refers to the explicit part of the mass transfer term and dmdtrefers to the implicit part of the term (lines 20 and 21 respectively). dmdtSign defines the directionof mass transfer for the phase pair.

The mass transfer coefficient is defined on lines 25-28. The mass transfer model used is definedat runtime in the phaseProperties file, see section 2.4.5. The method OpenFOAM uses to determineK is outlined in Prasad (2016).

It should be noted that the ”key” referred to in this file is the key assigned to the phase pairin the hash table. For cases with multiple phases this phase pair key makes it easier to choose andassign variables.

1 forAllConstIter2 (3 hashedWordList,4 compositionModel.species(),5 memberIter6 )7 {8 const word& member = ∗memberIter;9

10 const word name11 (12 IOobject::groupName(member, phase.name())13 ) ;1415 const word otherName16 (17 IOobject::groupName(member, otherPhase.name())18 ) ;1920 const volScalarField KD21 (22 K∗compositionModel.D(member)

48


23 ) ;2425 const volScalarField Yf26 (27 compositionModel.Yf(member, Tf)28 ) ;

The second forAllConstIter loop is nested within the interfaceCompositionModel forAllConstIterloop. This loop will evaluate the effect of mass transfer for every compositionModel for each speciesinvolved. The KD object created on line 20 is calculated by multiplying the mass transfer coefficientdefined in the previous section by the mass diffusivity, D for the component in the phase. Thefunction to determine the mass diffusivity is located ininterfacialCompositionModels/interfaceCompositionModels/InterfaceCompositionModels/

.../InterfaceCompositionModel.C

The species saturation concentration, Y_f is defined on line 25. The Yf function of the compo-sitionModel object is used on line 27. This value is very important in the calculation of the masstransfer for the system as it is the primary driving force for phase change. This function will bediscussed in section 3.5.

1 // Implicit transport through the phase2 ∗eqns[name] +=3 phase.rho()∗KD∗Yf4 − fvm::Sp(phase.rho()∗KD, eqns[name]−>psi());56 // Sum the mass transfer rate7 dmdtExplicit += dmdtSign∗phase.rho()∗KD∗Yf;8 dmdt −= dmdtSign∗phase.rho()∗KD∗eqns[name]−>psi();9

10 // Explicit transport out of the other phase11 if (eqns.found(otherName))12 {13 ∗eqns[otherName] −=14 otherPhase.rho()∗KD∗compositionModel.dY(member, Tf);15 }16 }17 }1819 return eqnsPtr;20 }

This section of the code is where the mass transfer term for the component in a phase is calculated.Multiplying out equation 1.14 yields the following equation

dmi

dt= ρϕkiϕaY

∗i − ρϕkiϕaYi (3.2)

Where kiϕa is KD in OpenFOAM.

This is the equation shown on lines 2-4. The function fvm::Sp on line 4 is used to make thesource term implicit. The function − > psi() is a reference to an unknown field. Line 4 is therefore,making an implicit source term based on the unknown variable in the eqns object, which will beYi. The massTransfer function ends by returning the eqnsPtr which is a pointer to a location whichcontains all the mass transfer terms for each component in each phase.

49


correctThermo Function

1 template<class BasePhaseSystem>2 void Foam::InterfaceCompositionPhaseChangePhaseSystem<BasePhaseSystem>::3 correctThermo()4 {5 BasePhaseSystem::correctThermo();67 // This loop solves for the interface temperatures, Tf, and updates the8 // interface composition models.9 //

10 // The rate of heat transfer to the interface must equal the latent heat11 // consumed at the interface, i .e .:12 //13 // H1∗(T1 − Tf) + H2∗(T2 − Tf) == mDotL14 // == K∗rho∗(Yfi − Yi)∗Li15 //16 // Yfi is likely to be a strong non−linear (typically exponential) function17 // of Tf, so the solution for the temperature is newton−accelerated1819 forAllConstIters( this−>phasePairs , phasePairIter)20 {21 const phasePair& pair = ∗(phasePairIter.object());2223 if (pair .ordered())24 {25 continue;26 }

The idea behind the correctThermo function is described in the comments of the function. The masstransfer occurring is resulting in a phase change which will result in a latent heat. The above sectiondescribes how the interface temperature will be affected by the latent heat. The forAllConstIterloop will solve for the interface temperature between all phase pairs in the system (line 19).

1 const phasePairKey key12(pair.first() , pair .second(), true) ;2 const phasePairKey key21(pair.second(), pair. first () , true) ;34 volScalarField H1(this−>heatTransferModels [pair][pair.first ()]−>K());5 volScalarField H2(this−>heatTransferModels [pair][pair.second()]−>K());6 dimensionedScalar HSmall(”small”, heatTransferModel::dimK, SMALL);78 volScalarField mDotL9 (

10 IOobject11 (12 ”mDotL”,13 this−>mesh().time().timeName(),14 this−>mesh()15 ) ,16 this−>mesh(),17 dimensionedScalar(dimEnergy/dimVolume/dimTime, Zero)18 ) ;19 volScalarField mDotLPrime20 (

50


21 IOobject22 (23 ”mDotLPrime”,24 this−>mesh().time().timeName(),25 this−>mesh()26 ) ,27 this−>mesh(),28 dimensionedScalar(mDotL.dimensions()/dimTemperature, Zero)29 ) ;3031 volScalarField& Tf = ∗this−>Tf [pair];

The objects key12 and key21 (lines 1 and 2) are used to define the direction of heat transfer. key12 denotes transfer from phase 1 to phase 2. The objects H1 and H2 (lines 4 and 5) are the heattransfer coefficients for phase 1 and 2 respectively. HSmall (line 6) is an object used to ensure thatthere is no division by zero. The mDotL object (line 8) energy released by latent heat due to masstransfer. It is the term on the right hand side of equation 1.8. The mDotLPrime object denotes thederivative of mDotL with respect to interface temperature, Tf . This term is employed in newtonsmethod to calculate Tf .

1 // Add latent heats from forward and backward models2 if ( this−>interfaceCompositionModels .found(key12))3 {4 this−>interfaceCompositionModels [key12]−>addMDotL5 (6 this−>massTransferModels [pair][pair.first()]−>K(),7 Tf,8 mDotL,9 mDotLPrime

10 ) ;11 }12 if ( this−>interfaceCompositionModels .found(key21))13 {14 this−>interfaceCompositionModels [key21]−>addMDotL15 (16 this−>massTransferModels [pair][pair.second()]−>K(),17 Tf,18 mDotL,19 mDotLPrime20 ) ;21 }

The addMDotL object is used if there is more than one species transferring phase. This variablewill sum up the individual mDotL values and store them.

1 // Update the interface temperature by applying one step of newton's2 // method to the interface relation3 Tf −=4 (5 H1∗(Tf − pair.phase1().thermo().T())6 + H2∗(Tf − pair.phase2().thermo().T())7 + mDotL8 )9 /(

10 max(H1 + H2 + mDotLPrime, HSmall)11 ) ;

51


1213 Tf.correctBoundaryConditions();1415 Info<< ”Tf.” << pair.name()16 << ”: min = ” << min(Tf.primitiveField())17 << ”, mean = ” << average(Tf.primitiveField())18 << ”, max = ” << max(Tf.primitiveField())19 << endl;2021 // Update the interface compositions22 if ( this−>interfaceCompositionModels .found(key12))23 {24 this−>interfaceCompositionModels [key12]−>update(Tf);25 }26 if ( this−>interfaceCompositionModels .found(key21))27 {28 this−>interfaceCompositionModels [key21]−>update(Tf);29 }30 }31 }

The interface temperature is then calculated using one step of newtons method on equation 1.8.The boundary conditions are corrected based on the new Tf value (line 13). The value for Tf is thenoutputted from the solver (line 15).

52

3.4. HEATANDMASSTRANSFERPHASESYSTEM CHAPTER 3. CLASSES

3.4 HeatAndMassTransferPhaseSystem

This section will discuss the HeatAndMassTransferPhaseSystem class. This class describes how themass transfer which was calculated in section 3.3.2 affects the momentum and energy equations.

3.4.1 HeatAndMassTransferPhaseSystem.H

1 #ifndef HeatAndMassTransferPhaseSystem H2 #define HeatAndMassTransferPhaseSystem H34 #include ”phaseSystem.H”56 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //78 namespace Foam9 {

1011 template<class modelType>12 class BlendedInterfacialModel;1314 class blendingMethod;15 class heatTransferModel;16 class massTransferModel;1718 /∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗\

19 Class HeatAndMassTransferPhaseSystem Declaration20 \∗−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−∗/

2122 template<class BasePhaseSystem>23 class HeatAndMassTransferPhaseSystem24 :25 public BasePhaseSystem26 {

The declaration file begins by declaring the phaseSystem header file and declaring the classes ofBlendedInterfacialModel, blendingMethod, heatTransferModel and massTransferModel. It is evidentfrom line 25 that the HeatAndMassTransferPhaseSystem exhibits inheritance from the BasePhas-eSystem (line 25) which is the templated class (line 22).

1 protected:23 // Protected typedefs45 typedef HashTable6 <7 HashTable8 <9 autoPtr<BlendedInterfacialModel<heatTransferModel>>

10 >,11 phasePairKey,12 phasePairKey::hash13 > heatTransferModelTable;

53


1415 typedef HashTable16 <17 HashTable18 <19 autoPtr<BlendedInterfacialModel<massTransferModel>>20 >,21 phasePairKey,22 phasePairKey::hash23 > massTransferModelTable;242526 // Protected data2728 //− Mass transfer rate29 HashPtrTable<volScalarField, phasePairKey, phasePairKey::hash>30 dmdt ;3132 //− Explicit part of the mass transfer rate33 HashPtrTable<volScalarField, phasePairKey, phasePairKey::hash>34 dmdtExplicit ;3536 //− Interface temperatures37 HashPtrTable<volScalarField, phasePairKey, phasePairKey::hash> Tf ;3839 // Sub Models4041 //− Heat transfer models42 heatTransferModelTable heatTransferModels ;4344 //− Mass transfer models45 massTransferModelTable massTransferModels ;

The heat transfer and mass transfer hash tables for the phase pairs are then defined and assignedthe type definition of heatTransferModelTable and massTransferModelTable respectively (lines 5-23). The heat transfer and mass transfer model objects are then of declared from the typedefs (lines42 and 45). The objects of Tf, dmdt and dmdtExplicit are declared as hash pointer tables (lines 29- 37).

1 // Member Functions23 //− Return true if there is mass transfer for phase4 virtual bool transfersMass(const phaseModel& phase) const;56 //− Return the interfacial mass flow rate7 virtual tmp<volScalarField> dmdt(const phasePairKey& key) const;89 //− Return the total interfacial mass transfer rate for phase

10 virtual tmp<volScalarField> dmdt(const phaseModel& phase) const;1112 //− Return the momentum transfer matrices13 virtual autoPtr<phaseSystem::momentumTransferTable>14 momentumTransfer() const;1516 //− Return the heat transfer matrices

54


17 virtual autoPtr<phaseSystem::heatTransferTable>18 heatTransfer() const;1920 //− Return the mass transfer matrices21 virtual autoPtr<phaseSystem::massTransferTable>22 massTransfer() const = 0;2324 //− Correct the thermodynamics25 virtual void correctThermo() = 0;2627 //− Read base phaseProperties dictionary28 virtual bool read();

Important member functions are then decalared. Note that the massTransfer and correctThermofunctions were described in section 3.3.2. The momentumTransfer and heatTransfer functions areresponsible for calculating the effect of mass transfer on the momentum and heat equations and aredescribed in section 3.4.2.

3.4.2 HeatAndMassTransferPhaseSystem.C

1 #include ”HeatAndMassTransferPhaseSystem.H”23 #include ”BlendedInterfacialModel.H”4 #include ”heatTransferModel.H”5 #include ”massTransferModel.H”67 #include ”HashPtrTable.H”89 #include ”fvcDiv.H”

10 #include ”fvmSup.H”11 #include ”fvMatrix.H”12 #include ”zeroGradientFvPatchFields.H”1314 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Constructors ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //1516 template<class BasePhaseSystem>17 Foam::HeatAndMassTransferPhaseSystem<BasePhaseSystem>::18 HeatAndMassTransferPhaseSystem19 (20 const fvMesh& mesh21 )22 :23 BasePhaseSystem(mesh)24 {25 this−>generatePairsAndSubModels26 (27 ”heatTransfer”,28 heatTransferModels29 ) ;3031 this−>generatePairsAndSubModels32 (33 ”massTransfer”,

55


34 massTransferModels35 ) ;

The constructor for the HeatAndMassTransferPhaseSystem starts by initializing the parent BasePhas-eSystem class (line 23). The heat transfer and mass transfer models are then generated for the systemon lines 25 and 31.

1 forAllConstIters( this−>phasePairs , phasePairIter)2 {3 const phasePair& pair = ∗(phasePairIter.object());45 if (pair .ordered())6 {7 continue;8 }9

10 // Initially assume no mass transfer1112 dmdt .set13 (14 pair ,15 new volScalarField16 (17 IOobject18 (19 IOobject::groupName(”dmdt”, pair.name()),20 this−>mesh().time().timeName(),21 this−>mesh(),22 IOobject::NO READ,23 IOobject::AUTO WRITE24 ) ,25 this−>mesh(),26 dimensionedScalar(dimDensity/dimTime, Zero)27 )28 ) ;2930 dmdtExplicit .set31 (32 pair ,33 new volScalarField34 (35 IOobject36 (37 IOobject::groupName(”dmdtExplicit”, pair.name()),38 this−>mesh().time().timeName(),39 this−>mesh()40 ) ,41 this−>mesh(),42 dimensionedScalar(dimDensity/dimTime, Zero)43 )44 ) ;4546 volScalarField H1(heatTransferModels [pair][pair. first ()]−>K());47 volScalarField H2(heatTransferModels [pair][pair.second()]−>K());

56


4849 Tf . set50 (51 pair ,52 new volScalarField53 (54 IOobject55 (56 IOobject::groupName(”Tf”, pair.name()),57 this−>mesh().time().timeName(),58 this−>mesh(),59 IOobject::NO READ,60 IOobject::AUTO WRITE61 ) ,62 (63 H1∗pair.phase1().thermo().T()64 + H2∗pair.phase2().thermo().T()65 )66 /max67 (68 H1 + H2,69 dimensionedScalar(”small”, heatTransferModel::dimK, SMALL)70 ) ,71 zeroGradientFvPatchScalarField::typeName72 )73 ) ;74 Tf [pair]−>correctBoundaryConditions();75 }76 }

The dmdt, dmdtExplicit and Tf objects are initialized on lines 12, 30 and 49 respectively. dmdtand dmdtExplicit are initially set to zero and are updated by the massTransfer function describedin section 3.3.2. The heat transfer coefficients, Hϕ are then computed by calling the K function ofthe heatTransferModels object for each phase (lines 46 and 47). The interface temperature, Tf, isthen initialized by manipulating the convection equation to isolate Tf, yielding the equation below.

Tf =HϕTϕ +Hϕ−1Tϕ−1

Hϕ +Hϕ−1

(3.3)

Where ϕ denotes the phase, and ϕ−1 denotes the other phase.

Momentum Transfer Function

1 template<class BasePhaseSystem>2 Foam::autoPtr<Foam::phaseSystem::momentumTransferTable>3 Foam::HeatAndMassTransferPhaseSystem<BasePhaseSystem>::momentumTransfer() const4 {5 autoPtr<phaseSystem::momentumTransferTable>6 eqnsPtr(BasePhaseSystem::momentumTransfer());78 phaseSystem::momentumTransferTable& eqns = eqnsPtr();9

10 // Source term due to mass transfer11 forAllConstIters( this−>phasePairs , phasePairIter)12 {

57


13 const phasePair& pair = ∗(phasePairIter.object());1415 if (pair .ordered())16 {17 continue;18 }1920 const volVectorField& U1(pair.phase1().U());21 const volVectorField& U2(pair.phase2().U());2223 const volScalarField dmdt(this−>dmdt(pair));24 const volScalarField dmdt21(posPart(dmdt));25 const volScalarField dmdt12(negPart(dmdt));2627 ∗eqns[pair .phase1().name()] += dmdt21∗U2 − fvm::Sp(dmdt21, U1);28 ∗eqns[pair .phase2().name()] −= dmdt12∗U1 − fvm::Sp(dmdt12, U2);29 }3031 return eqnsPtr;32 }

The momentum transfer function is responsible for calculating the momentum transferred betweenthe phases as a result of mass transfer. The function starts by initializing a pointer to a momentumtransfer table (line 6). The reference object, eqns, is then created by referencing the pointer (line 8).Lines 20 and 21 create the velocity objects and lines 24 and 25 create the objects which contain thedirection of mass transfer. It should be noted that for dmdt21, the mass transfer direction is fromphase two to phase one and dmdt12 is the reciprocal. The momentum change as a result of masstransfer is then calculated in lines 27 and 28 and stored in the eqns object for the phases. It is evi-dent that the the solver is employing equation 1.3 to evaluate the mass transfer effect on momentum.

Heat Transfer Function

1 template<class BasePhaseSystem>2 Foam::autoPtr<Foam::phaseSystem::heatTransferTable>3 Foam::HeatAndMassTransferPhaseSystem<BasePhaseSystem>::heatTransfer() const4 {5 auto eqnsPtr = autoPtr<phaseSystem::heatTransferTable>::New();6 auto& eqns = ∗eqnsPtr;78 for (const phaseModel& phase : this−>phaseModels )9 {

10 eqns.set11 (12 phase.name(),13 new fvScalarMatrix(phase.thermo().he(), dimEnergy/dimTime)14 ) ;15 }

The heat transfer function is responsible for calculating the energy transferred between the phasesas a result of mass transfer. Mass transfer results in phase change which will change the temperatureat the interface. Therefore, energy will transfer between phases in two different ways, the first isdue to a temperature difference, the second is due to kinetic energy contained in the mass beingtransferred. The heat transfer function begins by initializing a new pointer to a heat transfer table(line 3). A reference object, eqns, is then created by referencing the pointer.

58


1 // Heat transfer with the interface2 forAllConstIters(heatTransferModels , heatTransferModelIter)3 {4 const phasePair& pair =5 ∗(this−>phasePairs [heatTransferModelIter.key()]);67 const phaseModel∗ phase = &pair.phase1();8 const phaseModel∗ otherPhase = &pair.phase2();9

10 const volScalarField& Tf(∗Tf [pair]) ;1112 const volScalarField K113 (14 heatTransferModelIter()[pair. first ()]−>K()15 ) ;16 const volScalarField K217 (18 heatTransferModelIter()[pair.second()]−>K()19 ) ;20 const volScalarField KEff21 (22 K1∗K223 /max24 (25 K1 + K2,26 dimensionedScalar(”small”, heatTransferModel::dimK, SMALL)27 )28 ) ;2930 const volScalarField∗ K = &K1;31 const volScalarField∗ otherK = &K2;3233 forAllConstIter(phasePair, pair , iter )34 {35 const volScalarField& he(phase−>thermo().he());36 volScalarField Cpv(phase−>thermo().Cpv());3738 ∗eqns[phase−>name()] +=39 (∗K)∗(Tf − phase−>thermo().T())40 + KEff/Cpv∗he − fvm::Sp(KEff/Cpv, he);4142 Swap(phase, otherPhase);43 Swap(K, otherK);44 }45 }

The phases and interface temperature are defined on lines 7-10. The heat transfer coefficients, K1and K2 are then defined by calling the K function of the heat transfer model. The energy transferredas a result of temperature difference is then calculated on lines 39-40 and added to the heat transfertable for the phase. The equation can be compared to equation 1.7. The terms of the equation online 40 are used to increase diagonal dominance in the energy equation to help convergence.

1 // Source term due to mass transfer2 forAllConstIters( this−>phasePairs , phasePairIter)

59


3 {4 const phasePair& pair = ∗(phasePairIter.object());56 if (pair .ordered())7 {8 continue;9 }

1011 const phaseModel& phase1 = pair.phase1();12 const phaseModel& phase2 = pair.phase2();1314 const volScalarField& he1(phase1.thermo().he());15 const volScalarField& he2(phase2.thermo().he());1617 const volScalarField& K1(phase1.K());18 const volScalarField& K2(phase2.K());1920 const volScalarField dmdt(this−>dmdt(pair));21 const volScalarField dmdt21(posPart(dmdt));22 const volScalarField dmdt12(negPart(dmdt));23 const volScalarField& Tf(∗Tf [pair]) ;2425 ∗eqns[phase1.name()] +=26 dmdt21∗(phase1.thermo().he(phase1.thermo().p(), Tf))27 − fvm::Sp(dmdt21, he1)28 + dmdt21∗(K2 − K1);2930 ∗eqns[phase2.name()] −=31 dmdt12∗(phase2.thermo().he(phase2.thermo().p(), Tf))32 − fvm::Sp(dmdt12, he2)33 + dmdt12∗(K1 − K2);34 }3536 return eqnsPtr;37 }

The phase, enthalpy and kinetic energy are defined on lines 11-18. The direction of mass transfer isthen defined on lines 21 and 22. Note that for dmdt21, the mass transfer direction is from phase twoto phase one and dmdt12 is the opposite. The kinetic energy change as a result of mass transfer isthen calculated and added to the heat transfer table for each phase. The equation can be comparedto equation 1.6. The first two terms of the equation on lines 26, 27, 31 and 32 are used to increasediagonal dominance in the energy equation and help convergence.

60

3.5. SATURATION MODEL CLASS CHAPTER 3. CLASSES

3.5 Saturation Model Class

Saturation models employed in reactingTwoPhaseEulerFoam are used to determine saturation con-centrations or temperatures at an interface. The saturated model is an interface composition modelwhich assumes the rate of mass transfer is based on a concentration difference between the satu-rated concentration at the interface and the actual concentration. A saturation model is then appliedwhich will determine the saturation pressure at the interface. This pressure is then converted to aconcentration and used to calculcate mass transfer. The files for the Saturated class are located inthe directory interfacialCompositionModels/interfaceCompositionModels/Saturated/.

Saturated.H

1 #include ”InterfaceCompositionModel.H”2 #include ”saturationModel.H”34 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //56 namespace Foam7 {89 class phasePair;

1011 namespace interfaceCompositionModels12 {13 protected:1415 // Private data1617 //− Saturated species name18 word saturatedName ;1920 //− Saturated species index21 label saturatedIndex ;2223 //− Saturation pressure model24 autoPtr<saturationModel> saturationModel ;

The file begins with the declaration files for IterfaceCompositionModel and saturationModel. Theclass phasePair is forward declared and a namespace ”interfaceCompositionModels” is created. Theobject saturationModel_ is a pointer of the class saturationModel.

Saturated.C

1 #include ”Saturated.H”23 // ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Private Member Functions ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //45 template<class Thermo, class OtherThermo>6 Foam::tmp<Foam::volScalarField>7 Foam::interfaceCompositionModels::Saturated<Thermo, OtherThermo>::wRatioByP() const8 {9 const dimensionedScalar Wi

10 (11 ”W”,

61


12 dimMass/dimMoles,13 this−>thermo .composition().W(saturatedIndex )14 ) ;1516 return Wi/this−>thermo .W()/this−>thermo .p();

The member function wRatioByP is the conversion factor used to convert saturation pressure tosaturation concentration. This conversion was described in section 1 and can be seen in equation1.17. Wi is the moleculat weight of the species (line 10). The thermo.W() function returns themolecular weight of the species. The this-> pointer is refering to the current phase. Thereforethis->thermo.W() is referring to the molecular weight of the phase.

1 template<class Thermo, class OtherThermo>2 Foam::tmp<Foam::volScalarField>3 Foam::interfaceCompositionModels::Saturated<Thermo, OtherThermo>::Yf4 (5 const word& speciesName,6 const volScalarField& Tf7 ) const8 {9 if (saturatedName == speciesName)

10 {11 return wRatioByP()∗saturationModel −>pSat(Tf);12 }

The Yf function determines the saturation concentration at the interface and is an important variablein determining mass transfer. It is evident from the above section of the file that Yf is determinedby converting a saturation pressure to a saturation concentration. The pSat function belongs to thesaturationModel class which is chosen at runtime.

62


3.5.1 Arden Buck saturation model

This section will describe the Arden Buck saturation model which was the saturation model selectedfor the tutorial case in section 2. The directory containing the saturation models in reactingT-woPhaseEulerFoam is interfacialCompositionModels/saturationModels/. Descriptions of thesaturation models can be found in table 2.4. The Arden Buck equation is used to correlate thesaturated moisture concentration of air to temperature.

Ps(T ) = 611.21exp((18.678− T

234.5)(

T

257.14 + T)) (3.4)

Where Ps(T ) is the saturation pressure in Pa and T is the temperature in oC

ArdenBuck.C

1 namespace Foam2 {3 namespace saturationModels4 {5 defineTypeNameAndDebug(ArdenBuck, 0);6 addToRunTimeSelectionTable(saturationModel, ArdenBuck, dictionary);7 }8 }9

10 static const Foam::dimensionedScalar zeroC(””, Foam::dimTemperature, 273.15);11 static const Foam::dimensionedScalar A(””, Foam::dimPressure, 611.21);12 static const Foam::dimensionedScalar B(””, Foam::dimless, 18.678);13 static const Foam::dimensionedScalar C(””, Foam::dimTemperature, 234.5);14 static const Foam::dimensionedScalar D(””, Foam::dimTemperature, 257.14);

The Arden Buck equation is added as a run time selectable on line 6 of the above section of the file.Lines 10 to 14 then define the objects to be used in the ArdenBuck class.

1 Foam::tmp<Foam::volScalarField>2 Foam::saturationModels::ArdenBuck::pSat3 (4 const volScalarField& T5 ) const6 {7 volScalarField TC(T − zeroC);89 return A∗exp(TC∗xByTC(TC));

10 }

The pSat function of the ArdenBuck class is shown above. Inputting the variables into the aboveequation yields equation 3.4. The pSat function is then employed by the Yf function to determinethe saturation concentration at the interface as described in section 3.5.

63

Chapter 4

Algorithm

This section will focus on how the ReactingTwoPhaseEulerFoam solver employs the classes describedin chapter 3 to solve the twoPhaseSystem equations.

4.1 createFields.H

1 Info<< ”Creating phaseSystem\n” << endl;23 autoPtr<twoPhaseSystem> fluidPtr4 (5 twoPhaseSystem::New(mesh)6 ) ;7 twoPhaseSystem& fluid = fluidPtr();

The twoPhaseSystem is constructed and is assigned the name fluid. The fluid object for the tu-torial case described in section 2 will have be a two phase system of type interfaceComposition-PhaseChangeTwoPhaseSystem. The individual phase models for the phase system are of type mul-tiComponentPhaseModel.

1 dimensionedScalar pMin2 (3 ”pMin”,4 dimPressure,5 fluid6 ) ;78 #include ”gh.H”9

10 volScalarField& p = fluid.phase1().thermo().p();1112 Info<< ”Reading field p rgh\n” << endl;13 volScalarField p rgh14 (15 IOobject16 (17 ”p rgh”,18 runTime.timeName(),19 mesh,20 IOobject::MUST READ,

64

4.1. CREATEFIELDS.H CHAPTER 4. ALGORITHM

21 IOobject::AUTO WRITE22 ) ,23 mesh24 ) ;

The file then creates the pressure and hydrostaticless pressure and gravity terms.

It should be noted that the object ”fluid” now contains all the information about the two-phasesystem and its individual phases. The reactingTwoPhaseEulerFoam solver is very convoluted andthe classes are layered on top of one another. This complicates navigation through the solver files.The table below contains a list of the locations of important objects used to solve the twoPhaseSys-tem for the case described in chapter 2. The file locations are given from the directory$FOAM_SOLVERS/multiphase/reactingEulerFoam

Object LocationUEqn() phaseSystems/phaseModel/MovingPhaseModel/MovingPhaseModel.CheEqn() phaseSystems/phaseModel/AnisothermalPhaseModel/AnisothermalPhaseModel.CYiEqn(Yi) phaseSystems/phaseModel/MultiComponentPhaseModel/MultiComponentPhaseModel.CmomentumTransfer() phaseSystems/PhaseSystems/MomentumTransferPhaseSystem/..

../MomentumTransferPhaseSystem.CheatTransfer() phaseSystems/PhaseSystems/HeatAndMassTransferPhaseSystem/..

../HeatAndMassTransferPhaseSystem.CmassTransfer() phaseSystems/PhaseSystems/InterfaceCompositionPhaseChangePhaseSystem/..

../InterfaceCompositionPhaseChangePhaseSystem.C

Table 4.1: The definition locations of important Variables in the interfaceCompositionPhaseChangeT-woPhaseSystem and multiComponentPhaseModel classes

65

4.2. CREATEFIELDREFS.H CHAPTER 4. ALGORITHM

4.2 createFieldRefs.H

The following file creates variables from the fluid object created in section 4.1.

1 phaseModel& phase1 = fluid.phase1();2 phaseModel& phase2 = fluid.phase2();34 volScalarField& alpha1 = phase1;5 volScalarField& alpha2 = phase2;67 volVectorField& U1 = phase1.U();8 surfaceScalarField& phi1 = phase1.phi();9 surfaceScalarField& alphaPhi1 = phase1.alphaPhi();

10 surfaceScalarField& alphaRhoPhi1 = phase1.alphaRhoPhi();1112 volVectorField& U2 = phase2.U();13 surfaceScalarField& phi2 = phase2.phi();14 surfaceScalarField& alphaPhi2 = phase2.alphaPhi();15 surfaceScalarField& alphaRhoPhi2 = phase2.alphaRhoPhi();16 surfaceScalarField& phi = fluid.phi() ;1718 rhoThermo& thermo1 = phase1.thermo();19 rhoThermo& thermo2 = phase2.thermo();2021 volScalarField& rho1 = thermo1.rho();22 const volScalarField& psi1 = thermo1.psi();2324 volScalarField& rho2 = thermo2.rho();25 const volScalarField& psi2 = thermo2.psi();2627 const IOMRFZoneList& MRF = fluid.MRF();28 fv :: options& fvOptions = fluid.fvOptions();

The phase models are assigned on lines 1 and 2. The phase fractions are assigned on lines 4 and 5.The phase velocities and fluxes are assigned on lines 7 - 16. The thermodynamic models are assignedon lines 18 and 19. The density and compressibilty are assigned on lines 21 - 25. Note that all of theabove information was located within the fluid object and that this file is assigning variables datato the make the information easier to access.

66

4.3. REACTINGTWOPHASEEULERFOAM.C CHAPTER 4. ALGORITHM

4.3 reactingTwoPhaseEulerFoam.C

The reactingTwoPhaseEulerFoam file starts by creating the objects required to solve the finitevolume calculations and the including declaration file for the two-phase system. See chapter 4introduction.

1 int main(int argc, char ∗argv [])2 {3 #include ”postProcess.H”45 #include ”addCheckCaseOptions.H”6 #include ”setRootCase.H”7 #include ”createTime.H”8 #include ”createMesh.H”9 #include ”createControl.H”

10 #include ”createTimeControls.H”11 #include ”createFields.H”12 #include ”createFieldRefs.H”1314 if (!LTS)15 {16 #include ”CourantNo.H”17 #include ”setInitialDeltaT.H”18 }1920 bool faceMomentum21 (22 pimple.dict() .lookupOrDefault(”faceMomentum”, false)23 ) ;2425 bool implicitPhasePressure26 (27 mesh.solverDict(alpha1.name()).lookupOrDefault28 (29 ”implicitPhasePressure”, false30 )31 ) ;

The application starts on line 1. Important declaration files which set up the case, post processingutilities and the time object are included on lines 3-12. Line 14 checks if local time stepping isoccuring and will include files if it is set to not occur.

Line 20 is a boolean which checks if faceMomentum is occurring. faceMomentum can be set atruntime. Weller stated in the OpenFOAM-Dev release notes on github that ”face momentum” isbeneficial for the Euler-Euler multiphase equations because it allows all forces to be treated in aconsistent manner at the cell faces which will increase the calculation stability, consistancy and ac-curacy. However, the momentum transport terms must also be interpolated to the cell-faces whichwill reduce the accuracy of the momentum transport terms. The user must decide if accuracy of themomentum transport terms are more important than the accuracy of the force balance. The facemomentum is switched off by default (line 22).

An option is available to solve for the phase 1 pressure implicitly should it be required. (line25).

67


1 Info<< ”\nStarting time loop\n” << endl;23 while (runTime.run())4 {5 #include ”readTimeControls.H”67 int nEnergyCorrectors8 (9 pimple.dict() .lookupOrDefault<int>(”nEnergyCorrectors”, 1)

10 ) ;1112 if (LTS)13 {14 #include ”setRDeltaT.H”15 if (faceMomentum)16 {17 #include ”setRDeltaTf.H”18 }19 }20 else21 {22 #include ”CourantNos.H”23 #include ”setDeltaT.H”24 }2526 runTime++;27 Info<< ”Time = ” << runTime.timeName() << nl << endl;

This section is all about setting up the time step and starting the time loop in the algorithm.

1 // −−− Pressure−velocity PIMPLE corrector loop2 while (pimple.loop())3 {4 fluid . solve () ;5 fluid . correct () ;67 #include ”YEqns.H”89 if (faceMomentum)

10 {11 #include ”pUf/UEqns.H”12 #include ”EEqns.H”13 #include ”pUf/pEqn.H”14 #include ”pUf/DDtU.H”15 }16 else17 {18 #include ”pU/UEqns.H”19 #include ”EEqns.H”20 #include ”pU/pEqn.H”21 }2223 fluid .correctKinematics();

68


2425 if (pimple.turbCorr())26 {27 fluid .correctTurbulence();28 }29 }3031 runTime.write();3233 runTime.printExecutionTime(Info);34 }3536 Info<< ”End\n” << endl;

The pressure-veloctity PIMPLE corrector loop is set up in this section of the file (line 2). Withinthe loop the first equation to be solved is the phase continuity equation 1.4. Line 4 calls the solvefunction of the twoPhaseSystem object called fluid. This function is defined in section 3.1.2 andemploys the MULES algorithm. Line 5 then calls the correct function of the fluid object. The correctfunction is inherited from the phaseSystem class. Its function is to correct the fluid properties otherthan the thermo and turbulence for the system.

Line 7 should not be confused as a header file. The YEqns.H file contains the section of the ap-plication which solves the species fraction equations within each phase and calculates the masstransfer in the system, see equation 1.9. This file will be further explained in section 4.4.

The files containing the forces and momentum equation will vary depending on whether facemo-mentum is selected. The case where face momentum is not selected will be examined. Line 18 thencalls the file pU/UEqns.H. This file solves the momentum equations described in equation 1.1 withoutthe effects of pressure, turbulent drag and the explicit part of the drag term. The momentum trans-fer function described in section 3.4.2 is called in this file. This function calculates the momentumchange in the phase as a result of mass transfer.

Line 19 calls the file pU/EEqns.H. This file solves the energy equation for the system and includes theheat transfer function described in section 3.4.2 and the correct thermo function described in section3.3.2. The heatTransfer function calculates the effect of mass transfer on the energy equation. Thechange in energy in the phase is due to a kinetic energy difference and temperature difference. ThecorrectThermo function calculates the new temperature at the phase interface after mass transferhas occurred.

Line 20 calls the file pU/pEqn.H. This file solves the pressure equation of the system and the termsomitted from pU/UEqns.H are included here. This is where the pressure-velocity linking occurs inthe system which is pivotal for the PIMPLE algorithm. Rusche(2002) should be consulted for moreinformation on the theory behind the pressure-velocity linking in the PISO algorithm.

The kinematics of the fluid are then corrected on line 23 and the turbulence properties are cor-rected on line 27. The file ends by writing the specified data to runtime (line 31), and printing thetime elapsed to the terminal window (line 33).

69

4.4. YEQNS.H CHAPTER 4. ALGORITHM

4.4 YEqns.H

1 autoPtr<phaseSystem::massTransferTable>2 massTransferPtr(fluid.massTransfer());34 phaseSystem::massTransferTable&5 massTransfer(massTransferPtr());67 PtrList<volScalarField>& Y1 = phase1.Y();8 PtrList<volScalarField>& Y2 = phase2.Y();

The file starts by defining a pointer to a mass transfer table called massTransferPtr. The pointer isthen initialized using the massTransfer function of the fluid object which is described in section 3.3.2.The object massTransfer is then initialised as a reference to the pointer. This process of calling afunction to return a pointer and then using a variable to reference the pointer is used bacause themass transfer table generated by the mass transfer function is large. It would slow the applicationdown to copy the object so in the interest of execution time the pointers are outputted from thefunction.

Y1 refers to the species in phase 1 and Y2 refers to the species in phase 2. For the tutorial casedescribed section 2, both Y1 and Y2 will have two species, gas and liquid.

1 forAll (Y1, i)2 {3 tmp<fvScalarMatrix> Y1iEqn(phase1.YiEqn(Y1[i]));45 if (Y1iEqn.valid())6 {7 Y1iEqn =8 (9 Y1iEqn

10 ==11 ∗massTransfer[Y1[i].name()]12 + fvOptions(alpha1, rho1, Y1[i])13 ) ;1415 Y1iEqn−>relax();16 Y1iEqn−>solve(mesh.solver(”Yi”));17 }18 }

The application continues and executes a for loop which will loop through all of the species in phase1. An fvScalarMatrix called Y1iEqn is then initialized with the species conservation equation for thespecies in the current iteration of the for loop (line 3). YiEqn function is defined in the phase model ofeach phase. Since both phases in the case were multiComponentPhaseModels, the YiEqn function isdefined in the file phaseSystems/phaseModel/MultiComponentPhaseModelMultiComponentPhaseModel.C.See section 4.4.1. Y1[i] is referring to the species in the current iteration of the for loop.

The YiEqn is then rewritten to include the mass transfer term in the species conservation equa-tion. The species equation now matches equation 1.12. The equation is relaxed and then solved forthe species concentration. The procedure will loop for every component in phase 1. The procedurethen occurs for phase 2.

70

4.4. YEQNS.H CHAPTER 4. ALGORITHM

4.4.1 MultiComponentPhaseModel.C

1 template<class BasePhaseModel>2 Foam::tmp<Foam::fvScalarMatrix>3 Foam::MultiComponentPhaseModel<BasePhaseModel>::YiEqn4 (5 volScalarField& Yi6 )7 {89 return

10 (11 fvm::ddt(alpha, rho, Yi)12 + fvm::div(alphaRhoPhi, Yi, ”div(” + alphaRhoPhi.name() + ”,Yi)”)13 − fvm::Sp(this−>continuityError(), Yi)1415 − fvm::laplacian16 (17 fvc :: interpolate (alpha)18 ∗fvc :: interpolate ( this−>turbulence().muEff()/Sc ),19 Yi20 )

The above equation is identical to the left hand side of equation 1.12.

71

Chapter 5

Case Modification

This chapter will look at using methanol as an alternative to water. In order for this to happenchanges will have to be made to the following files in the case set up.

File name0/water.gas0/water.liquid0/T.gas0/T.liquidconstant/phasePropertiesconstant/thermophysicalProperties.gasconstant/thermophysicalProperties.liquid

Table 5.1: Case files requiring changing

The only composition model in the system which requires changing is the saturation model as it isonly valid for humid air. This model will be changed to the Antoine saturation model. However, thecurrent Antoine saturation model available in reactingTwoPhaseEulerFoam relates pressure to tem-perature via an exponential scale. For the antoine coefficients obtained for methanol, a power scaleis required. Therefore a new saturation model must be created.Before proceeding the reactingEuler-Foam directory must be copied to the user directory.

The current Antoine saturation model available in reactingEulerFoam is outlined below.

log(Ps(T )) = A+B

C + T(5.1)

Where Ps(T ) is the saturation pressure in bar, T is the temperature in K and A, B and C are thespecies coefficients which have units of dimensionless, K and K, respectively.

The new Antoine Equation is shown below.

log10(Ps(T )) = A− B

C + T(5.2)

Manipulations and calculus are performed on the above equations to explicitly describe differentvariables. Member functions are called which calculate and return the variables.

72

5.1. ANTOINE EQUATION MANIPULATIONS CHAPTER 5. CASE MODIFICATION

5.1 Antoine Equation Manipulations

Isolating the saturation pressure, Ps, in equation 5.2 yields the equation below. This equation isused to calculate the saturation concentration in the manner described in section 3.5.

Ps = 10A− BC+T (5.3)

Equation 5.3 is then differentiated with respect to temperature and yields the equation below,

dPsdT

=log 10 ∗B(C + T )

2 Ps (5.4)

Equation 5.2 is once again manipulated and the saturation temperature, Ts, is isolated. This termis used as part of the driving force for mass transfer in the thermal phase change model.

Ts =B

A− log10 P− C (5.5)

5.2 Copying solver to the user directory

foamcp −r −−parents applications/solvers/multiphase/reactingEulerFoam/

$WM PROJECT USER DIRcd $WM PROJECT USER DIR/applications/solvers/multiphase/reactingEulerFoamrm −rf reactingMultiphaseEulerFoammv reactingTwoPhaseEulerFoam/ myReactingTwoPhaseEulerFoam/sed −i s/reactingTwoPhaseEulerFoam/myReactingTwoPhaseEulerFoam/g Allw∗sed −i /”reactingMultiphaseEulerFoam\/Allwclean”/d Allwcleansed −i /”reactingMultiphaseEulerFoam\/Allwmake\ \$targetType\ \$∗”/d Allwmakesed −i s/reactingTwoPhaseEulerFoam/myReactingTwoPhaseEulerFoam/g

myReactingTwoPhaseEulerFoam/Make/filessed −i s/FOAM APPBIN/FOAM USER APPBIN/g myReactingTwoPhaseEulerFoam/Make/filesmv myReactingTwoPhaseEulerFoam/reactingTwoPhaseEulerFoam.C

myReactingTwoPhaseEulerFoam/myReactingTwoPhaseEulerFoam.C./Allwclean./Allwmake

5.3 Creating a new saturation model

The most efficient way to create the new antoine model is to copy the old model and modify themember functions using the equations described in section 5.1.

cp −rf interfacialCompositionModels/saturationModels/Antoine interfacialCompositionModels/saturationModels/AntoineConventional

sed −i s/Antoine/AntoineConventional/g interfacialCompositionModels/saturationModels/AntoineConventional/∗

mv interfacialCompositionModels/saturationModels/AntoineConventional/Antoine.CinterfacialCompositionModels/saturationModels/AntoineConventional/AntoineConventional.C

73

5.3. CREATING A NEW SATURATION MODEL CHAPTER 5. CASE MODIFICATION

mv interfacialCompositionModels/saturationModels/AntoineConventional/Antoine.HinterfacialCompositionModels/saturationModels/AntoineConventional/AntoineConventional.H

Next it is necessary to tell the solver that there is another saturation model available. Edit the fileinterfacialCompositionModels/Make/files and include the link to the AntoineConventionalmodel below the Antoine model in the file. The interfacialCompositionModels directory shouldthen be compiled.

wclean interfacialCompositionModelswmake interfacialCompositionModels

Replace the AntoineConventional.C file with the code below.

#include ”AntoineConventional.H”#include ”addToRunTimeSelectionTable.H”#include ”function1.H”

// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Static Data Members ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

namespace Foam{namespace saturationModels{

defineTypeNameAndDebug(AntoineConventional, 0);addToRunTimeSelectionTable(saturationModel, AntoineConventional, dictionary);

}}

// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Constructors ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

Foam::saturationModels::AntoineConventional::AntoineConventional(const dictionary& dict):

saturationModel(),A (”A”, dimless, dict) ,B (”B”, dimTemperature, dict),C (”C”, dimTemperature, dict)

{}

// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Destructor ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

Foam::saturationModels::AntoineConventional::˜AntoineConventional(){}

// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ Member Functions ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

Foam::tmp<Foam::volScalarField>Foam::saturationModels::AntoineConventional::pSat(

const volScalarField& T) const{

return

74

5.4. NEW CASE SETUP CHAPTER 5. CASE MODIFICATION

dimensionedScalar(”one”, dimPressure, 1)∗100000∗pow(10,(A − B /(C + T)));

}

Foam::tmp<Foam::volScalarField>Foam::saturationModels::AntoineConventional::pSatPrime(


return pSat(T)∗B ∗log(dimensionedScalar(”one”, dimless, 1)∗10)/pow((C + T),2);

}

Foam::tmp<Foam::volScalarField>Foam::saturationModels::AntoineConventional::lnPSat(


return log(pSat(T));}

Foam::tmp<Foam::volScalarField>Foam::saturationModels::AntoineConventional::Tsat(

const volScalarField& p) const{

returnB /(A − log10(p∗dimensionedScalar(”one”, dimless/dimPressure, 1)))− C ;

}

5.4 New Case Setup

Copy the original case described in section 2 and remove all the time files and other files which arenot required.

cp −rf bubbleColumnEvaporatingDissolving methanolColumncd methanolColumnrm −rf 0 0.∗ [1−9]∗ constant/polyMesh

The files which require changing are outlined in table 5.1. The first two files can be quickly changedas illustrated below.

mv water.gas methanol.gasmv water.liquid methanol.liquid

The files in the constant folder will need to be replace with the files below.

75


5.4.1 constant/thermophysicalProperties.gas

FoamFile{

version 2.0;format ascii ;class dictionary ;location ”constant”;object thermophysicalProperties.gas;

}// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

thermoType{

type heRhoThermo;mixture multiComponentMixture;transport const;thermo hConst;equationOfState perfectGas;specie specie ;energy sensibleInternalEnergy;

}

dpdt yes;

species(

airmethanol

) ;

inertSpecie air ;

”(mixture|air)”{

specie{

molWeight 28.9;}thermodynamics{

Hf 0;Cp 1012.5;

}transport{

mu 1.84e−05;Pr 0.7;

}}

methanol{

specie

76


{molWeight 32.01;

}thermodynamics{

Hf −6.2938e+06;Cp 1380.6;

}transport{

mu 1.84e−05;Pr 0.7;

}}

5.4.2 constant/thermophysicalProperties.liquid

FoamFile{

version 2.0;format ascii ;class dictionary ;location ”constant”;object thermophysicalProperties.liquid ;

}// ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ ∗ //

thermoType{

type heRhoThermo;mixture multiComponentMixture;transport const;thermo hConst;equationOfState perfectFluid;specie specie ;energy sensibleInternalEnergy;

}

dpdt yes;

species(

airmethanol

) ;

inertSpecie methanol;

”(mixture|methanol)”{

specie{

molWeight 32.01;}

77

5.5. RUN NEW CASE CHAPTER 5. CASE MODIFICATION

equationOfState{

R 3000;rho0 764; //Methanol at 55 C from Engineering ToolBox

}thermodynamics{

Hf −7.4467e+06;Cp 2686; //Methanol at 55 C from Engineering ToolBox

}transport{

mu 3.99e−4; //Methanol at 55 C from Engineering ToolBoxPr 5.3; //k = 0.202 W/m/K thermal conductivity. Pr = mu Cp / k

}}

air{

specie{

molWeight 28.9;}equationOfState{

R 3000;rho0 764; //Methanol at 55 C from Engineering ToolBox

}thermodynamics{

Hf 0;Cp 2686; //Methanol at 55 C from Engineering ToolBox

}transport{

mu 3.99e−4; //Methanol at 55 C from Engineering ToolBoxPr 5.3; //k = 0.202 W/m/K thermal conductivity. Pr = mu Cp / k

}}

5.4.3 constant/phaseProperties

File very long. To be downloaded.

5.5 Run new case

The case can now be run in the same manner as in section 2.7. generate the mesh using theblockMesh utilty.

cp −rf 0orig 0blockMeshsetFieldsreactingTwoPhaseEulerFoam >& log&paraFoam

78

5.5. RUN NEW CASE CHAPTER 5. CASE MODIFICATION

It is possible to see the methanol transferring from the liquid to the gas phase in paraview. To dothis select methanol.gas from the fields tab in the properties section. Click apply. The methanol.gasfield then needs to be selected in the main drop down menu above the viewing window. Press playand watch the mass transfer.

79

Study questions

1. In what file is the twoPhaseSystem for a case set?

2. What type of twoPhaseSystem would be used to simulate a condensor?

3. In which file are the typedefs of the twoPhaseSystem located?

4. In which file are the typedefs of the phaseModels located?

80

a detailed descrption of reactingtwophaseeulerfoam

Documents